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On Anisotropic Regularity Criteria for the Solutions to 3D Navier–Stokes Equations

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Abstract

In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide sufficient conditions for the regularity of strong solutions in terms of certain components of the velocity gradient. Based on the recent results from Kukavica (J Math Phys 48(6):065203, 2007) we show these conditions as anisotropic regularity criteria which partially interpolate results from Kukavica (J Math Phys 48(6):065203, 2007) and older results of similar type from Penel and Pokorný (Appl Math 49(5):483–493, 2004).

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Correspondence to Patrick Penel.

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Communicated by G.P. Galdi

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Penel, P., Pokorný, M. On Anisotropic Regularity Criteria for the Solutions to 3D Navier–Stokes Equations. J. Math. Fluid Mech. 13, 341–353 (2011). https://doi.org/10.1007/s00021-010-0038-6

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