Topics in Mathematical Fluid Mechanics

Cetraro, Italy 2010, Editors: Hugo Beirão da Veiga, Franco Flandoli

Author: Peter Constantin,Arnaud Debussche,Giovanni P. Galdi,Michael Růžička,Gregory Seregin

Publisher: Springer

ISBN: 3642362974

Category: Mathematics

Page: 313

View: 6559

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.

Mathematical Topics in Fluid Mechanics

Volume 1: Incompressible Models

Author: Pierre-Louis Lions

Publisher: OUP Oxford

ISBN: 9780199679218

Category: Mathematics

Page: 252

View: 8782

One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no central core theory. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models.

Mathematical Fluid Mechanics

Recent Results and Open Questions

Author: Jiri Neustupa,Patrick Penel

Publisher: Birkhäuser

ISBN: 3034882432

Category: Mathematics

Page: 269

View: 5230

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models

Author: Pierre-Louis Lions

Publisher: Oxford University Press on Demand

ISBN: 9780198514886

Category: Mathematics

Page: 348

View: 8648

Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

Mathematical Topics in Fluid Mechanics

Author: Jose Francisco Rodrigues,Adelia Sequeira

Publisher: CRC Press

ISBN: 9780582209541

Category: Mathematics

Page: 280

View: 1419

This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

Mathematical Fluid Dynamics, Present and Future

Tokyo, Japan, November 2014

Author: Yoshihiro Shibata,Yukihito Suzuki

Publisher: Springer

ISBN: 4431564578

Category: Mathematics

Page: 613

View: 3193

This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

Topics in Fluid Mechanics

Author: René Chevray,Jean Mathieu

Publisher: Cambridge University Press

ISBN: 9780521422727

Category: Science

Page: 320

View: 1285

This book offers a novel but unified treatment of an established subject. Rather than describe the standard topics in fluid mechanics in traditional form, the book presents each topic as part of a wider class of problems so that a unity of concepts is emphasized over a unity of material.

Mathematical Analysis in Fluid Mechanics: Selected Recent Results

Author: Raphaël Danchin,Reinhard Farwig,Jiří Neustupa,Patrick Penel

Publisher: American Mathematical Soc.

ISBN: 1470436469

Category: Fluid mechanics

Page: N.A

View: 8007

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 Topics in Fluid Mechanics: Volume 1: Incompressible Models

Author: Pierre-Louis Lions

Publisher: Clarendon Press

ISBN: 9780198514879

Category: Science

Page: 252

View: 765

One of the most challenging topics in applied mathematics over the past decades has been the development of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc. lead to such equations when formulated in mathematical terms. However despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contains many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena.

Advances in Mathematical Fluid Mechanics

Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday

Author: Rolf Rannacher,Adélia Sequeira

Publisher: Springer Science & Business Media

ISBN: 9783642040689

Category: Mathematics

Page: 657

View: 1747

The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the ?eld of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, re?ecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 21–25, 2007 and organized on the oc- sion of Professor Galdi’s 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian ?ow problems, with special emphasis on hydrodynamic stability and ?uid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down signi?cant milestones in these ?elds, with a great in?uence on interdis- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through int- lectual guidance and others indirectly by pairing them with well chosen senior c- laborators. A brief review of Professor Galdi’s activities and some impressions by colleagues and friends are included here.

An Introduction to Theoretical Fluid Mechanics

Author: Stephen Childress

Publisher: American Mathematical Soc.

ISBN: 0821848887

Category: Science

Page: 201

View: 5124

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Selected Topics of Computational and Experimental Fluid Mechanics

Author: Jaime Klapp,Gerardo Ruíz Chavarría,Abraham Medina Ovando,Abel López Villa,Leonardo Di G. Sigalotti

Publisher: Springer

ISBN: 3319114875

Category: Science

Page: 548

View: 6182

This book contains invited lectures and selected contributions presented at the Enzo Levi and XIX Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2013. It is aimed at fourth year undergraduate and graduate students, and scientists in the fields of physics, engineering and chemistry who are interested in fluid dynamics from an experimental and theoretical point of view. The invited lectures are introductory and avoid the use of complicated mathematics. The fluid dynamics applications include multiphase flow, convection, diffusion, heat transfer, rheology, granular material, viscous flow, porous media flow, geophysics and astrophysics. The material contained in the book includes recent advances in experimental and theoretical fluid dynamics and is suitable for both teaching and research.

Fundamental Directions in Mathematical Fluid Mechanics

Author: Giovanni P. Galdi,John G. Heywood,Rolf Rannacher

Publisher: Birkhäuser

ISBN: 3034884249

Category: Mathematics

Page: 293

View: 9823

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.

Lectures on Topological Fluid Mechanics

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 2 - 10, 2001

Author: Mitchell A. Berger,Renzo L. Ricca,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners

Publisher: Springer

ISBN: 3642008372

Category: Science

Page: 223

View: 8423

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Advances in Mathematical Fluid Mechanics

Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999

Author: Josef Malek,Jindrich Necas,Mirko Rokyta

Publisher: Springer Science & Business Media

ISBN: 3642573088

Category: Mathematics

Page: 236

View: 2562

This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Contributions to Current Challenges in Mathematical Fluid Mechanics

Author: Giovanni P. Galdi,Malcolm I. Heywood,Rolf Rannacher

Publisher: Springer Science & Business Media

ISBN: 9783764371043

Category: Science

Page: 152

View: 2803

This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct

Introduction to Mathematical Fluid Dynamics

Author: Richard E. Meyer

Publisher: Courier Corporation

ISBN: 0486458873

Category: Science

Page: 184

View: 5459

This introduction to the behavior of liquids and gases is geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. It offers excellent coverage of kinematics, momentum principle and ideal fluid, Newtonian fluid, fluids of small viscosity, and aspects of rotating fluids and compressibility. 1971 edition.