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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
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SYSNO ASEP 0502440 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior Author(s) Novotný, A. (FR)
Petzeltová, Hana (MU-W) RID, SAISource Title Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. - Cham : Springer, 2018 / Giga Y. ; Novotný A. - ISBN 978-3-319-13343-0 Pages s. 1381-1546 Number of pages 166 s. Number of copy 500 Number of pages 3045 Publication form Print - P Language eng - English Country CH - Switzerland Keywords Navier-Stokes equations Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 EID SCOPUS 85054405157 DOI 10.1007/978-3-319-13344-7_76 Annotation This double-sized chapter contains two related themes that were supposed to be covered by two independent chapters of the handbook in the original project: (1) weak solutions of the Navier-Stokes equations in the barotropic regime and (2) weak solutions of the Navier-Stokes-Fourier system. We shall discuss for both systems: (1)Various notions of weak solutions, their relevance, and their mutual relations. (2)Global existence of weak solutions. (3)Notions of relative energy functional, dissipative solutions and relative energy inequality and its impact on the investigation of the stability analysis of compressible flows. (4)Weak strong uniqueness principle. (5)Longtime behavior of weak solutions. For physical reasons, we shall limit ourselves to the three-dimensional physical space. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
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