Cauchy problem of the magnetohydrodynamic Burgers system

Hai Yang Jin, Zhian Wang, Linjie Xiong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)127-151
Number of pages25
JournalCommunications in Mathematical Sciences
Volume13
Issue number1
Publication statusPublished - 1 Jan 2014

Keywords

  • MHD Burgers system
  • Nonlinear stability
  • Rarefaction waves
  • Viscous shock waves
  • Weighted energy estimates

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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