Author: James SerrinPublisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 40
Book Description
On the Interior Regularity of Weak Solutions of the Navier-stokes Equations
Author: James SerrinPublisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 40
Book Description
On the Interior Regularity of Weak Solutions of the Stationary Navier-Stokes Equations
Author: Joachim NaumannRemarks on the Regularity of Weak Solutions of the Navier-Stokes Equations
Author: Dongho ChaePublisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 21
Book Description
The Navier-Stokes Equations
Author: Hermann SohrPublisher: Springer Science & Business Media
ISBN: 3034805519
Category : Mathematics
Languages : en
Pages : 376
Book Description
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.
A Type of Gevrey Class Regularity of Weak Solutions of the Navier-stokes Equations
Author: Dongho ChaeTrends in Partial Differential Equations of Mathematical Physics
Author: José F. RodriguesPublisher: Springer Science & Business Media
ISBN: 3764373172
Category : Mathematics
Languages : en
Pages : 290
Book Description
This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.
Mathematical Fluid Mechanics
Author: Jiri NeustupaPublisher: Springer Science & Business Media
ISBN: 9783764365936
Category : Mathematics
Languages : en
Pages : 288
Book Description
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.
On the Regularity of Weak Solutions of the Equations of Navier-Stokes
Author: H. SohrNavier-Stokes Equations
Author: Roger TemamPublisher: American Mathematical Soc.
ISBN: 0821827375
Category : Mathematics
Languages : en
Pages : 426
Book Description
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.
Author: Grigorij A. Seregin