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Regularity criterion for solutions of three-dimensional turbulent channel flows. (English) Zbl 1151.76012
Summary: We consider the three-dimensional Navier-Stokes equations in infinite channel. We provide a regularity criterion for solutions of the three-dimensional Navier-Stokes equations in terms of the vertical component of the velocity field.
MSC:
76F02Fundamentals of turbulence
35B65Smoothness and regularity of solutions of PDE
35Q35PDEs in connection with fluid mechanics
76D03Existence, uniqueness, and regularity theory
76D05Navier-Stokes equations (fluid dynamics)