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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]

In this paper, we consider the $$n$$ -dimensional ( $$n\ge 2$$ ) damped models of incompressible fluid mechanics in Besov spaces and establish the global (in time) regularity of classical solutions provided that the initial data are suitable small. [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 global regularity of the two-dimensional generalized incompressible magnetohydrodynamics system with velocity dissipation exponent and magnetic diffusion exponent based on the improved integrability in terms of vorticity. This result is a further improvement of very recent works (Jiu and Zhao (2014) and Yamazaki (2013)) which require and . Therefore our result is more closer to the resolution of the well-known global regularity issue on the 2D magnetohydrodynamics system . [Copyright &y& Elsevier]