Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data

  • In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point.

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Metadaten
Author:Huicheng Yin
URN:urn:nbn:de:kobv:517-opus-26263
Series (Serial Number):Preprint ((2002) 07)
Document Type:Preprint
Language:English
Date of Publication (online):2008/11/11
Year of Completion:2002
Publishing Institution:Universität Potsdam
Release Date:2008/11/11
Tag:compressible Euler equations; lifespan; nondegenerate condition; shock wave
RVK - Regensburg Classification:SI 990
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Collections:Universität Potsdam / Schriftenreihen / Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis
Universität Potsdam / Schriftenreihen / Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis / 2002
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:
Die Printversion kann in der Universitätsbibliothek Potsdam eingesehen werden:
Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis, 1997-

Die Online-Fassung wird auf der Homepage des Instituts für Mathematik veröffentlicht.