An improved pressure regularity criterion of magnetohydrodynamic equations in critical Besov spaces

This paper is concerned with an improved pressure regularity criterion of the three-dimensional (3D) magnetohydrodynamic (MHD) equations in the largest critical Besov spaces. Based on the Littlewood-Paley decomposition technique, the weak solutions are proved to be smooth if the pressure lies in the largest critical Besov spaces, \(\pi(x,t) \in L^{p}(0,T;\dot{B}^{0}_{q,r}(\mathbf{R}^{3}))\) for \(\frac{2}{p}+\frac{3}{q}=2\), \(1\leq r\leq\frac{2q}{3}\), \(\frac{3}{2}< q\leq\infty\).