Recent Topics On Mathematical Theory Of Viscous Incompressible Fluid

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Recent Topics On Mathematical Theory Of Viscous Incompressible Fluid
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Author : Hideo Kozono
language : en
Publisher:
Release Date : 1998
Recent Topics On Mathematical Theory Of Viscous Incompressible Fluid written by Hideo Kozono and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Fluid dynamics categories.
Mathematical Theory Of A Fluid Flow Around A Rotating And Translating Body
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Author : Šárka Nečasová
language : en
Publisher: Springer Nature
Release Date : 2025-07-01
Mathematical Theory Of A Fluid Flow Around A Rotating And Translating Body written by Šárka Nečasová and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-01 with Mathematics categories.
The book deals with qualitative analysis of the mathematical model of flow of a viscous incompressible fluid around a translating and rotating body. The considered mathematical model, which represents the description of the flow in a coordinate system attached to the body, is derived from the Navier–Stokes equations by means of an appropriate transformation. The core of the book is the mathematical theory of the transformed equations. Most of the text is devoted to the theory of the linearized versions of these equations (i.e. the Stokes- and Oseen-type equations), because they play a fundamental role in the theory of the complete nonlinear system. Considering strong, weak, and very weak solutions, we present the L2 and Lq theories and the weighted space theory (with Muckenhaupt's weights) in the whole space and in an exterior domain. The book also contains the spectral analysis of the associated linear Stokes-Oseen-type operators and the information on semigroups generated by these operators, and related resolvent estimates. Moreover, the book describes the asymptotic behavior of solutions and leading profiles of solutions for linear and as well as nonlinear systems. Further, the book contains studies of the problem with artificial boundary (important in numerical analysis), an introduction to the theory of the corresponding complete nonlinear system in both steady and nonsteady cases, a brief description of the situation when the rotation is not parallel to the velocity at infinity and necessary estimates of the related Oseen kernels.
Recent Developments Of Mathematical Fluid Mechanics
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Author : Herbert Amann
language : en
Publisher: Birkhäuser
Release Date : 2016-03-17
Recent Developments Of Mathematical Fluid Mechanics written by Herbert Amann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-17 with Mathematics categories.
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.
Some Current Topics On Nonlinear Conservation Laws
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Author : Ling Hsiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Some Current Topics On Nonlinear Conservation Laws written by Ling Hsiao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of $-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics. This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis. Titles in this series are co-published with International Press, Cambridge, MA.
Mathematical Fluid Dynamics Present And Future
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Author : Yoshihiro Shibata
language : en
Publisher: Springer
Release Date : 2016-12-01
Mathematical Fluid Dynamics Present And Future written by Yoshihiro Shibata and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
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.
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models
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Author : Franck Boyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models written by Franck Boyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
New Directions In Mathematical Fluid Mechanics
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Author : Andrei V. Fursikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-11
New Directions In Mathematical Fluid Mechanics written by Andrei V. Fursikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-11 with Science categories.
On November 3, 2005, Alexander Vasil’evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov’s contributions to science is provided in the following article “Scienti?c portrait of Alexander Vasil’evich Kazhikhov”. This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.
Dynamics Of Viscous Compressible Fluids
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Author : Eduard Feireisl
language : en
Publisher: Oxford University Press
Release Date : 2004
Dynamics Of Viscous Compressible Fluids written by Eduard Feireisl and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Language Arts & Disciplines categories.
This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.
Mathematical Topics In Fluid Mechanics
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Author : Jose Francisco Rodrigues
language : en
Publisher: CRC Press
Release Date : 2020-10-02
Mathematical Topics In Fluid Mechanics written by Jose Francisco Rodrigues and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.
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.
Nonlinear Problems In Mathematical Physics And Related Topics I
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Author : Michael Sh. Birman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Problems In Mathematical Physics And Related Topics I written by Michael Sh. Birman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday. O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences. Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva. Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role. Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary. Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.