Mathematical analysis of the Navier-Stokes equations : Cetraro, Italy 2017 / Matthias Hieber, James C. Robinson, Yoshihiro Shibata ; Giovanni P. Galdi, Yoshihiro Shibata, editors.
Lecture notes in mathematics (Springer-Verlag). CIME Foundation subseries [More in this series]
Lecture notes in mathematics, 0075-8434 ; 2254. CIME Foundation subseries
Notes
"This principal objective of the CIME School on "Mathematical Aspects of the Navier-Stokes Equations: foundations and overview of basic open problems," in Cetraro, September 4-8 2017, was to provide series of lectures devoted to several fundamental and diverse aspects of the Navier-Storkes equations. The present volume collects some of them, ..."--Preface
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."--Back cover.
Bibliographic references
Includes bibliographical references.
Contents
Analysis of viscous fluid flows : an approach by evolution equations / Matthias Hieber
Partial regularity for the 3D Navier-Stokes equations / James C. Robinson
R boundedness, maximal regularity and free boundary problems for the Navier Stokes Equations / Yoshihiro Shibata.
ISBN
9783030362256
3030362256
OCLC
1183727303
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