Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/35496
Title: Cauchy problem of the magnetohydrodynamic burgers system
Authors: Jin, HY
Wang, ZA 
Xiong, L
Keywords: MHD Burgers system
Nonlinear stability
Rarefaction waves
Viscous shock waves
Weighted energy estimates
Issue Date: 2014
Publisher: International Press
Source: Communications in mathematical sciences, 2014, v. 13, no. 1, p. 127-151 How to cite?
Journal: Communications in mathematical sciences 
Abstract: In this paper, the asymptotic nonlinear stability of solutions to the Cauchy problem of a strongly coupled Burgers system arising in magnetohydrodynamic (MHD) turbulence [Fleischer and Diamond (2000), Yanase (1997)] is established. It is shown that, as time tends to infinity, the solutions of the Cauchy problem converge to constant states or rarefaction waves with large data, or viscous shock waves with arbitrarily large amplitude, where the precise asymptotic behavior depends on the relationship between the left and right end states of the initial value. Our results confirm the existence of shock waves (or turbulence) numerically found in [Fleischer and Diamond (2000), Yanase (1997)].
URI: http://hdl.handle.net/10397/35496
ISSN: 1539-6746 (print)
1945-0796 (online)
DOI: 10.4310/CMS.2015.v13.n1.a7
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