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)].
Original language | English |
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Pages (from-to) | 127-151 |
Number of pages | 25 |
Journal | Communications in Mathematical Sciences |
Volume | 13 |
Issue number | 1 |
Publication status | Published - 1 Jan 2014 |
Keywords
- MHD Burgers system
- Nonlinear stability
- Rarefaction waves
- Viscous shock waves
- Weighted energy estimates
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics