On the Global Regularity Problem for 3-dimensional Navier-Stokes Equations
Author: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
Published: 1995
Total Pages:
ISBN-13:
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Author: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
Published: 1995
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Vadim Gene Bondarevsky
Publisher:
Published: 1996
Total Pages: 114
ISBN-13:
DOWNLOAD EBOOKAuthor: James C. Robinson
Publisher: Cambridge University Press
Published: 2016-09-07
Total Pages: 487
ISBN-13: 1107019664
DOWNLOAD EBOOKAn accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
Author: Terence Tao
Publisher:
Published: 2006
Total Pages: 284
ISBN-13:
DOWNLOAD EBOOKProviding an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
Author: Hermann Sohr
Publisher: Springer Science & Business Media
Published: 2012-12-13
Total Pages: 376
ISBN-13: 3034805519
DOWNLOAD EBOOKThe 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.
Author: Hajer Bahouri
Publisher: Springer Science & Business Media
Published: 2011-01-03
Total Pages: 530
ISBN-13: 3642168302
DOWNLOAD EBOOKIn recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Author: James C. Robinson
Publisher: Cambridge University Press
Published: 2016-01-21
Total Pages: 247
ISBN-13: 131658934X
DOWNLOAD EBOOKThe 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.
Author: Charles R. Doering
Publisher: Cambridge University Press
Published: 1995
Total Pages: 236
ISBN-13: 9780521445689
DOWNLOAD EBOOKThis 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.
Author: James Serrin
Publisher:
Published: 1961
Total Pages: 40
ISBN-13:
DOWNLOAD EBOOKAuthor: Terence Tao
Publisher: Springer
Published: 2016-08-29
Total Pages: 366
ISBN-13: 9811017891
DOWNLOAD EBOOKThis is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.