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Some criteria concerning the vorticity and the problem of global regularity for the 3D Navier-Stokes equations. (English) Zbl 1205.35186

Summary: We review some results concerning the problem of global-in-time regularity for the initial boundary value problem for the Navier-Stokes equations in three-dimensional domains. In particular, we focus on sufficient conditions on the vorticity field which imply that strong (hence smooth) solutions exist on arbitrary time intervals.

MSC:

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