Cauchy problem for an isentropic magnetogasdynamic system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Fu, Xiaoyu¹  Sharma, V. D.² 

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

关键词: Quasi linear hyperbolic system;    Cauchy problem;    Global solution;    Magnetogasdynamics;   

DOI  :  10.1016/j.jmaa.2014.11.024

来源: Elsevier

【 摘 要 】

This paper investigates the Cauchy problem for an isentropic magnetogasdynamic system. Under certain reasonable hypotheses on the initial data, we obtain the global existence and uniqueness of the C-1 solution to the system. Meanwhile, when the hypotheses on the initial data do not hold, we obtain the blow-up phenomena of the C-1 solution to the system. The bounds of the solution are shown to depend on the parameter nu, which characterizes a one-dimensional plane flow (nu = 0) or a three-dimensional cylindrically symmetric flow (nu = 1); it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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