Author: Joachim NaumannPublisher:
ISBN:
Category :
Languages : en
Pages : 39
Book Description
On the Interior Regularity of Weak Solutions of the Stationary Navier-Stokes Equations
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
Very Weak Solutions of the Stationary Navier–Stokes Equations for an Incompressible Fluid Past Obstacles
Author: 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.
Lecture Notes On Regularity Theory For The Navier-stokes Equations
Author: Gregory SereginPublisher: World Scientific
ISBN: 9814623423
Category : Mathematics
Languages : en
Pages : 269
Book Description
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.
Local Regularity of Suitable Weak Solutions to the Navier-Stokes Equations Near the Boundary
Author: Grigorij A. SereginRemarks 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
Handbook of Mathematical Fluid Dynamics
Author: S. FriedlanderPublisher: Elsevier
ISBN: 0080478301
Category : Science
Languages : en
Pages : 725
Book Description
This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.
Author: Chung Ki Cho
Author: Dongho Chae