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Regularity criteria for the three-dimensional Navier-Stokes equations. (English) Zbl 1159.35053
Summary: We consider the three-dimensional Navier-Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one component of the velocity field, or alternatively in terms of one component of the pressure gradient, for the regularity of strong solutions to the three-dimensional Navier-Stokes equations.
MSC:
35Q30Stokes and Navier-Stokes equations
76D05Navier-Stokes equations (fluid dynamics)
76D03Existence, uniqueness, and regularity theory