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Mathematical Analysis of the Navier-Stokes Equations - Cetraro, Italy 2017 (Paperback, 1st ed. 2020)
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Mathematical Analysis of the Navier-Stokes Equations - Cetraro, Italy 2017 (Paperback, 1st ed. 2020)
Series: C.I.M.E. Foundation Subseries, 2254
Expected to ship within 10 - 15 working days
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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.
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