Cargando…

Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Galdi, Giovanni, Shibata, Yoshihiro
Lenguaje:eng
Publicado: Springer 2020
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-36226-3
http://cds.cern.ch/record/2717275
_version_ 1780965601606369280
author Galdi, Giovanni
Shibata, Yoshihiro
author_facet Galdi, Giovanni
Shibata, Yoshihiro
author_sort Galdi, Giovanni
collection CERN
description 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.
id cern-2717275
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2020
publisher Springer
record_format invenio
spelling cern-27172752021-04-22T06:30:47Zdoi:10.1007/978-3-030-36226-3http://cds.cern.ch/record/2717275engGaldi, GiovanniShibata, YoshihiroMathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open ProblemsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:27172752020
spellingShingle Mathematical Physics and Mathematics
Galdi, Giovanni
Shibata, Yoshihiro
Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title_full Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title_fullStr Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title_full_unstemmed Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title_short Mathematical Analysis of the Navier-Stokes Equations : Foundations and Overview of Basic Open Problems
title_sort mathematical analysis of the navier-stokes equations : foundations and overview of basic open problems
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-36226-3
http://cds.cern.ch/record/2717275
work_keys_str_mv AT galdigiovanni mathematicalanalysisofthenavierstokesequationsfoundationsandoverviewofbasicopenproblems
AT shibatayoshihiro mathematicalanalysisofthenavierstokesequationsfoundationsandoverviewofbasicopenproblems