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Remarks on regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure. (English) Zbl 1284.35313

In this article the author proves a regularity criterion on the gradient of pressure for weak solutions of the Navier-Stokes equation in \({\mathbb R}^3\). If the gradient of pressure belongs to \(L^{\frac{2}{3-r}}((0,T);\dot X_r({\mathbb R}^3)^3)\), where \(X_r({\mathbb R}^3)\) is a suitable multiplier space with \(0<r<1\), then the weak solution is actually regular.

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35D30 Weak solutions to PDEs
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