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In this paper we investigate the regularity criterion for the local in time classical solution to the 3D incompressible magnetohydrodynamic equations. We prove that if ∇ × u belongs to L 2 ( 0 , T ; B ̇ ∞ , ∞ − 1 ) , then the local solution ( u , B ) can be extended beyond time T . As a consequence, this result extends several previous works. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove the global regularity to the Cauchy problem of 3D incompressible magnetohydrodynamic- (MHD- ) model with fractional diffusion. We prove that if the exponents and satisfy with , then the 3D MHD- model with fractional diffusion admits a unique global smooth solution. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the inviscid 3D Boussinesq system in Besov spaces and obtain the lower bound for the lifespan of solutions. [Copyright &y& Elsevier]