A remark on blow-up criterion for 3D compressible magnetohydrodynamic flows with vacuum

摘要

In this paper, we concerned a blowup criterion of strong solutions for 3D viscous, compressible magnetohydrodynamic(MHD) flows with vacuum. We proved that any strong solutions of viscous, compressible MHD fluids will blow up in finite time if limT→T*(∥ρ∥L∞(0,T;Ls)+∥H∥L∞(0,T;Ll))=∞, for some 1 < s < ∞ large enough, and 245≤l≤∞, provided that the viscosity coefficients satisfy 3μ > λ. This work is motivated by the recent works of Wang and Li (2014) and Yu (2013) on blow up criterion for 3D MHD flows.