Download or read book Numerical Study on the Regularity of the Navier Stokes Equations written by Mark Dowker and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes On Regularity Theory For The Navier stokes Equations written by Gregory Seregin and published by World Scientific. This book was released on 2014-09-16 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.
Download or read book Navier Stokes Equations and Nonlinear Functional Analysis written by Roger Temam and published by SIAM. This book was released on 1995-01-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.
Download or read book Navier Stokes Equations written by Roger Temam and published by Elsevier. This book was released on 2016-06-03 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.
Download or read book Navier Stokes Equations written by Roger Temam and published by American Mathematical Soc.. This book was released on 2001-04-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.
Download or read book On the Numerical Analysis of the Nonstationary Navier Stokes Equations written by R. Rannacher and published by . This book was released on 1989 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Analysis of the Navier Stokes Equations written by Charles R. Doering and published by Cambridge University Press. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.
Download or read book Navier Stokes Equations and Nonlinear Functional Analysis written by Roger Temam and published by SIAM. This book was released on 1995-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.
Download or read book On the numerical analysis of the nonstationary Navier Stokes equations written by Rolf Rannacher and published by . This book was released on 1989 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis of the Navier Stokes Equations written by Matthias Hieber and published by Springer Nature. This book was released on 2020-04-28 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
Download or read book The Navier Stokes Equations written by Hermann Sohr and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
Download or read book The Navier Stokes Equations Theory and Numerical Methods written by John G. Heywood and published by Springer. This book was released on 2006-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
Download or read book The Navier Stokes Equations written by Rodolfo Salvi and published by CRC Press. This book was released on 2001-09-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."
Download or read book Recent Progress in the Theory of the Euler and Navier Stokes Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2016-01-21 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
Download or read book Lectures on Navier Stokes Equations written by Tai-Peng Tsai and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.
Download or read book Numerical Study of the Navier Stokes Equations in Three Dimensions written by Padam Jain and published by . This book was released on 1967 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: To investigate the process of energy transfer from large eddies to smaller ones at high Reynolds Numbers, a finite difference method is used to obtain the periodic solutions of the Navier-Stokes equations in three dimensions when the initial motion is assumed to be v sub 1 = cos x sin y sin z, v sub 2 = -sin x cos y sin z, v sub 3 = 0. A numerical technique for the solution of Poisson's equation for the three dimensional problem is described and used for the solution of the problem. Mean kinetic energy and mean square vorticity are calculated and it is found that the numerical method provides estimates of these quantities up to a time of the order of 2. The structure of the turbulent flow is investigated by a study of the velocity correlation function R sub ij. (Author).
Download or read book Navier Stokes Equations and Related Nonlinear Problems written by Herbert Amann and published by VSP. This book was released on 1998-01-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of invited lectures and contributed papers which were delivered at the Sixth International Conference on Navier-Stokes Equations and Related Nonlinear Problems, held in Palanga, Lithuania, 22-29 May 1997. While the emphasis was on the mathematical foundation of fluid dynamics, related contributions on nonlinear and numerical analysis were discussed as well. The topics covered include: incompressible fluids described by Navier-Stokes equations, compressible fluids, non-Newtonian fluids, free boundary problems, equations from thermo- and magnetohydrodynamcis, asymptotic analysis, stability, and related problems of nonlinear and numerical analysis.
