| 书目名称 | Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents | | 编辑 | Alex Kaltenbach | | 视频video | | | 概述 | Includes the first proof of the existence of weak solutions of the unsteady p(t,x)-Navier-Stokes equations.Provides a comprehensive review of the rapidly expanding field of unsteady problems with vari | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | 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 f | | 出版日期 | Book 2023 | | 关键词 | Existence of Weak Solutions; Variable Exponent Lebesgue Spaces; Variable Exponent Bochner-Lebesgue Spa | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-29670-3 | | isbn_softcover | 978-3-031-29669-7 | | isbn_ebook | 978-3-031-29670-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 18:12:31
