Global smooth solutions for the compressible viscous and heat-conductive gas

Authors:
Yuming Qin, Guili Hu and Taige Wang

Journal:
Quart. Appl. Math. **69** (2011), 509-528

MSC (2000):
Primary 35B41

DOI:
https://doi.org/10.1090/S0033-569X-2011-01218-0

Published electronically:
May 6, 2011

MathSciNet review:
2850743

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the global existence of smooth solutions to a system of equations describing one-dimensional motion of a self-gravitating, radiative and chemically reactive gas. We have proved that for any arbitrary large smooth initial data, the problem under consideration admits a unique globally smooth (classical) solution. Our results have improved those results by Umehara and Tani ([J. Differential Equations, ** 234**(2007), 439-463; Proc. Japan Acad., **84**, Ser. A(2008), 123-128]) and also by Qin, Hu, Huang, and Ma.

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Additional Information

**Yuming Qin**

Affiliation:
Department of Applied Mathematics, Donghua University, Shanghai 201620, People’s Republic of China

Email:
yuming_qin@hotmail.com

**Guili Hu**

Affiliation:
College of Sciences, Donghua University, Shanghai 201620, People’s Republic of China

Email:
hgl-8507@163.com

**Taige Wang**

Affiliation:
College of Sciences, Donghua University, Shanghai 201620, People’s Republic of China

Email:
tigerwtg@hotmail.com

DOI:
https://doi.org/10.1090/S0033-569X-2011-01218-0

Keywords:
Global solution; free-boundary problem; self-gravitation; radiative gas; reactive gas; Lagrangian mass coordinate.

Received by editor(s):
January 4, 2010

Published electronically:
May 6, 2011

Additional Notes:
The authors were supported in part by the NNSF Grant of China #10871040.

Article copyright:
© Copyright 2011
Brown University

The copyright for this article reverts to public domain 28 years after publication.