Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Nonlinear stability of spherical self-similar flows to the compressible Euler equations


Authors: Seung-Yeal Ha, Hsiu-Chuan Huang and Wen-Ching Lien
Journal: Quart. Appl. Math. 72 (2014), 109-136
MSC (2010): Primary 35LXX, 76NXX
DOI: https://doi.org/10.1090/S0033-569X-2013-01329-9
Published electronically: December 31, 2013
MathSciNet review: 3185135
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Abstract: We present the nonlinear stability of spherical self-similar flows arising from the uniform expansion of a spherical piston toward still gas. If the perturbation of the expansion speed of the piston is sufficiently small compared with the strength of the leading shock, a global weak solution of the isentropic compressible Euler system exists in the region between the spherical piston and the leading shock under the structural condition on the shock Mach number and the nondimensional piston speed. Moreover, we show that the perturbed flow tends to the corresponding self-similar flow time-asymptotically. Our analysis is based on the modified Glimm scheme.


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Additional Information

Seung-Yeal Ha
Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea
Email: syha@snu.ac.kr

Hsiu-Chuan Huang
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan City 70101, Taiwan
Email: hchuan@mail.ncku.edu.tw

Wen-Ching Lien
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan City 70101, Taiwan
Email: wlien@mail.ncku.edu.tw

DOI: https://doi.org/10.1090/S0033-569X-2013-01329-9
Keywords: Euler equations, shock waves, self-similarity, Glimm scheme
Received by editor(s): April 1, 2012
Published electronically: December 31, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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