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

Published online by Cambridge University Press:  22 January 2016

Huicheng Yin
Huicheng Yin*
Affiliation:
Department of Mathematics and IMS, Nanjing University, Nanjing 210093, P. R. China, huicheng@nju.edu.cn
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Abstract

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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 satisfy certain nondegeneracy conditions, then from the results in [22], we know that there exists a unique blowup point at the blowup time such that the first order derivatives of a smooth solution blow up, while 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 a 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 a neighbourhood of the blowup point.

Keywords

35L7035L65
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 175 , 2004 , pp. 125 - 164
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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