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On the regularity conditions for the Navier-Stokes and related equations. (English) Zbl 1130.35100
The authors derive regularity conditions for the solutions of generalized Navier-Stokes equations with fractional powers \(\alpha\) of the Laplacian, in the case \(0< \alpha \leq 2\). It is shown that the regularity assumption of the direction field of the vorticity compensates with the integrability condition for the magnitude of vorticity.

MSC:
35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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