Kaltenbach Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents

1. Auflage 2023
ISBN: 978-3-031-29670-3
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 358 Seiten

Reihe: Lecture Notes in Mathematics

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 andnon-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.

Zielgruppe

Research

Autoren/Hrsg.

Kaltenbach, Alex

Inhaltsverzeichnis

- 1. Introduction. - 2. Preliminaries. - Part I Main Part. - 3. Variable Bochner–Lebesgue Spaces. - 4. Solenoidal Variable Bochner–Lebesgue Spaces. - 5. Existence Theory for Lipschitz Domains. - Part II Extensions. - 6. Pressure Reconstruction. - 7. Existence Theory for Irregular Domains. - 8. Existence Theory for p- < 2. - 9. Appendix.

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