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Conditions of Prodi-Serrin’s type for local regularity of suitable weak solutions to the Navier-Stokes equations. (English) Zbl 1090.35148

The author studies conditions under which the solution to the Navier-Stokes equations has better properties in the neighborhood of a point in the time-space. He proves certain alternative to the regularity criterion given in (J. Nečas and J. Neustupa [J. Math. Fluid Mech. 4, No. 3, 237–256 (2002; Zbl 1010.35081)]); the regularity criterion requires certain higher integrability of the velocity and of the pressure in a parabolic neighborhood of the studied point.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids

Citations:

Zbl 1010.35081
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