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A new regularity criterion for the 3D incompressible MHD equations in terms of one component of the gradient of pressure. (English) Zbl 1256.35060

Summary: We study the global regularity issue for the 3D incompressible MHD equations. It is proved that if the pressure \(P\) satisfies \(\partial_3 P\in L^\beta(0,T; L^\mu(\mathbb{R}^3))\), with \({2\over \beta}+{3\over \mu}\leq 2\), \(3\leq \mu<+\infty\) and \(1<\beta<+\infty\), then the corresponding weak solution \((u,b)\) is regular on \([0,T]\).

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
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