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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 06141096
In this article the author proves a regularity criterion on the gradient of pressure for weak solutions of the Navier-Stokes equation in 3 . If the gradient of pressure belongs to L 2 3-r ((0,T);X ˙ r ( 3 ) 3 ), where X r ( 3 ) is a suitable multiplier space with 0<r<1, then the weak solution is actually regular.
MSC:
35Q30Stokes and Navier-Stokes equations
35B65Smoothness and regularity of solutions of PDE
76D05Navier-Stokes equations (fluid dynamics)
35D30Weak solutions of PDE