Format:
1 Online-Ressource(XIII, 358 p. 11 illus. in color.)
Edition:
1st ed. 2023.
ISBN:
9783031296703
Series Statement:
Lecture Notes in Mathematics 2329
Content:
This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
Additional Edition:
ISBN 9783031296697
Additional Edition:
ISBN 9783031296710
Additional Edition:
Erscheint auch als Druck-Ausgabe Kaltenbach, Alex Pseudo-monotone operator theory for unsteady problems with variable exponents Cham, Switzerland : Springer, 2023 ISBN 9783031296697
Language:
English
Keywords:
Partielle Differentialgleichung
;
Navier-Stokes-Gleichung
;
Hochschulschrift
DOI:
10.1007/978-3-031-29670-3
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