GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

Abstract

Abstract: In this paper, we study the three-dimensional incompressible magnetohydrodynamic equations in a smooth bounded domains, in which the viscosity of the fluid and the magnetic diffusivity are concerned with density. The existence of global strong solutions is established in vacuum cases, provided the assumption that (||▽μ(ρ₀)||_L^p +||▽ν(ρ₀)||_L^q +||b₀||_L³+||ρ₀||_L^∞) (p, q > 3) is small enough, there is not any smallness condition on the velocity.

Key words: incompressible MHD, global solution, small initial data

Defu CHEN, Xia YE. GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS[J].Acta mathematica scientia,Series B, 2018, 38(6): 1833-1845.

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