On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation

Abstract

Abstract In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear estimates in BMO space, Young’s inequality, cancellation property, interpolation inequality) and delicate energy estimates, we establish an improved blow-up criterion for the strong solution. Moreover, we also obtain the existence of the strong solution for small initial data, the smallness conditions of which are given by the suitable Sobolev norms.

Keywords

• Hall-magnetohydrodynamics
• Blow-up criterion
• BMO norms
• Small initial data
• Partial dissipation