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Global Cauchy problem of 2D generalized magnetohydrodynamic equations

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.jmaa.2014.06.030
Keywords
  • Partial Differential Equations

Abstract

Abstract In this paper we prove the global-in-time existence of smooth solutions of the 2D generalized magnetohydrodynamic equations with zero viscosity, when the power of the Laplacian operator −Δ in the dissipation term of the induction equation is between 1 and 2. We also show a regularity criterion on the direction of the magnetic field b0:=b|b| when β=1.

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