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Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations. (English) Zbl 1075.35031

Summary: We consider the Cauchy problem for the \(n\)-dimensional Navier-Stokes equations and we prove a regularity criterion for weak solutions involving the summability of the pressure. Related results for the initial-boundary value problem are also presented.

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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