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Existence Theory For Generalized Newtonian Fluids

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Existence Theory for Generalized Newtonian Fluids

Existence Theory for Generalized Newtonian Fluids Book
Author : Dominic Breit
Publisher : Academic Press
Release : 2017-03-22
ISBN : 0128110457
Language : En, Es, Fr & De

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Book Description :

Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs. Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids Book
Author : Martin Fuchs,Gregory Seregin
Publisher : Springer
Release : 2007-05-06
ISBN : 3540444424
Language : En, Es, Fr & De

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Book Description :

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

Recent Advances in Partial Differential Equations and Applications

Recent Advances in Partial Differential Equations and Applications Book
Author : Vicenţiu D. Rădulescu,Adélia Sequeira,Vsevolod A. Solonnikov
Publisher : American Mathematical Soc.
Release : 2016-06-28
ISBN : 1470415216
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids Book
Author : Martin Fuchs,Gregory Seregin
Publisher : Springer
Release : 2000-12-12
ISBN : 9783540413974
Language : En, Es, Fr & De

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Book Description :

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

New Trends and Results in Mathematical Description of Fluid Flows

New Trends and Results in Mathematical Description of Fluid Flows Book
Author : Miroslav Bulíček,Eduard Feireisl,Milan Pokorný
Publisher : Springer
Release : 2018-09-26
ISBN : 331994343X
Language : En, Es, Fr & De

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Book Description :

The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.

Three Dimensional Navier Stokes Equations for Turbulence

Three Dimensional Navier Stokes Equations for Turbulence Book
Author : Luigi C. Berselli
Publisher : Academic Press
Release : 2021-03-26
ISBN : 0128219459
Language : En, Es, Fr & De

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Book Description :

Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work

Topics in Mathematical Fluid Mechanics

Topics in Mathematical Fluid Mechanics Book
Author : Peter Constantin,Arnaud Debussche,Giovanni P. Galdi,Michael Růžička,Gregory Seregin
Publisher : Springer
Release : 2013-04-03
ISBN : 3642362974
Language : En, Es, Fr & De

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Book Description :

This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.

Nonlinear Elliptic and Parabolic Problems

Nonlinear Elliptic and Parabolic Problems Book
Author : Michel Chipot
Publisher : Springer Science & Business Media
Release : 2005-10-18
ISBN : 9783764372668
Language : En, Es, Fr & De

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Book Description :

The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Mathematical Aspects of Fluid Mechanics

Mathematical Aspects of Fluid Mechanics Book
Author : James C. Robinson,José L. Rodrigo,Witold Sadowski
Publisher : Cambridge University Press
Release : 2012-10-18
ISBN : 1139577212
Language : En, Es, Fr & De

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Book Description :

The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Nonlinear Problems in Mathematical Physics and Related Topics

Nonlinear Problems in Mathematical Physics and Related Topics Book
Author : Olʹga Aleksandrovna Ladyzhenskai︠a︡
Publisher : Springer Science & Business Media
Release : 2002
ISBN : 9780306474224
Language : En, Es, Fr & De

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Book Description :

The main topics in this volume reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results. One of the main topics considered is the set of Navier-Stokes equations and their solutions.

Mathematical Analysis of Viscoelastic Flows

Mathematical Analysis of Viscoelastic Flows Book
Author : Michael Renardy
Publisher : SIAM
Release : 2000-01-01
ISBN : 9780898719413
Language : En, Es, Fr & De

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Book Description :

This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.

Electrorheological Fluids Modeling and Mathematical Theory

Electrorheological Fluids  Modeling and Mathematical Theory Book
Author : Michael Ruzicka
Publisher : Springer
Release : 2007-05-06
ISBN : 3540444270
Language : En, Es, Fr & De

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Book Description :

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

Evolution PDEs with Nonstandard Growth Conditions

Evolution PDEs with Nonstandard Growth Conditions Book
Author : Stanislav Antontsev,Sergey Shmarev
Publisher : Springer
Release : 2015-04-01
ISBN : 9462391122
Language : En, Es, Fr & De

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Book Description :

This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.

Handbook of Differential Equations Evolutionary Equations

Handbook of Differential Equations  Evolutionary Equations Book
Author : C.M. Dafermos,Milan Pokorny
Publisher : Elsevier
Release : 2008-10-06
ISBN : 9780080931975
Language : En, Es, Fr & De

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Book Description :

The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area - Continuation of previous volumes in the handbook series covering Evolutionary PDEs - Written by leading experts

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences Book
Author : Riccardo Sacco,Giovanna Guidoboni,Aurelio Giancarlo Mauri
Publisher : Academic Press
Release : 2019-07-18
ISBN : 0128125195
Language : En, Es, Fr & De

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Book Description :

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical engineering and the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book employs computational models as synthesized tools for the investigation, quantification, verification, and comparison of different conjectures or scenarios of the behavior of a given compartment of the human body under physiological and pathological conditions. Presents theoretical (modeling), biological (experimental), and computational (simulation) perspectives Features examples, exercises, and MATLAB codes for further reader involvement Covers basic and advanced functional and computational techniques throughout the book

Mathematical Analysis in Fluid Mechanics Selected Recent Results

Mathematical Analysis in Fluid Mechanics  Selected Recent Results Book
Author : Raphaël Danchin,Reinhard Farwig,Jiří Neustupa,Patrick Penel
Publisher : American Mathematical Soc.
Release : 2018-06-26
ISBN : 1470436469
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)—Complex Fluids and the Issue of Regularity, held from May 8–12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids. Topics of different kinds of solutions, boundary conditions, and interfaces are also discussed.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Lectures on Visco Plastic Fluid Mechanics

Lectures on Visco Plastic Fluid Mechanics Book
Author : Guillaume Ovarlez,Sarah Hormozi
Publisher : Springer
Release : 2018-06-26
ISBN : 3319894382
Language : En, Es, Fr & De

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Book Description :

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid models mathematical modeling of flows of visco-plastic fluids computing flows of visco-plastic fluids rheology of visco-plastic fluids and visco-plastic suspensions application of visco-plastic fluids in engineering sciences complex flows of visco-plastic fluids.

Non Newtonian Fluids

Non Newtonian Fluids Book
Author : Boling Guo,Chunxiao Guo,Yaqing Liu,Qiaoxin Li
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2018-10-08
ISBN : 3110549611
Language : En, Es, Fr & De

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Book Description :

This book provides an up-to-date overview of mathematical theories and research results in non-Newtonian fluid dynamics. Related mathematical models, solutions as well as numerical experiments are discussed. Fundamental theories and practical applications make it a handy reference for researchers and graduate students in mathematics, physics and engineering. Contents Non-Newtonian fluids and their mathematical model Global solutions to the equations of non-Newtonian fluids Global attractors of incompressible non-Newtonian fluids Global attractors of modified Boussinesq approximation Inertial manifolds of incompressible non-Newtonian fluids The regularity of solutions and related problems Global attractors and time-spatial chaos Non-Newtonian generalized fluid and their applications

Fluid Structure Interaction and Biomedical Applications

Fluid Structure Interaction and Biomedical Applications Book
Author : Tomáš Bodnár,Giovanni P. Galdi,Šárka Nečasová
Publisher : Springer
Release : 2014-10-13
ISBN : 3034808224
Language : En, Es, Fr & De

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Book Description :

This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine.