Pseudo-monotone operator theory for unsteady problems with variable exponents

• Verfasst von: Kaltenbach, Alex [VerfasserIn]
• Titel: Pseudo-monotone operator theory for unsteady problems with variable exponents
• Institutionen: Springer Nature Switzerland AG [Verlag]
• Institutionen: Albert-Ludwigs-Universität Freiburg [Grad-verleihende Institution]
• Verf.angabe: Alex Kaltenbach
• Verlagsort: Cham, Switzerland
• Verlag: Springer
• E-Jahr: 2023
• Jahr: [2023]
• Umfang: xiii, 355 Seiten
• Illustrationen: Illustrationen, Diagramme
• Gesamttitel/Reihe: Lecture notes in mathematics ; volume 2329
• Hochschulschrift: Dissertation, University of Freiburg, 2021
• ISBN: 978-3-031-29669-7
• DOI: doi:10.1007/978-3-031-29670-3
• Schlagwörter: (s)Partielle Differentialgleichung / (s)Navier-Stokes-Gleichung
• Dokumenttyp: Hochschulschrift
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Online-Ausgabe: Kaltenbach, Alex: Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents. - 1st ed. 2023.. - Cham : Springer International Publishing, 2023. - 1 Online-Ressource(XIII, 358 p. 11 illus. in color.)
• K10plus-PPN: 1858034337

Abstract

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.