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Remarks on the smoothness of the \(L^\infty(0,T;L^3)\) solutions of the 3-D Navier-Stokes equations. (English) Zbl 0896.35102

Summary: We consider the \(L^\infty(0,T; L^3(\Omega))\) solutions of the Navier-Stokes equations, where \(\Omega\) is a domain of \(\mathbb{R}^3\). We give a very simple proof of a sufficient condition for regularity of solutions. This condition contains, as a quite particular case, continuity from the left on \((0, T]\) with values in \(L^3(\Omega)\).

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
35K55 Nonlinear parabolic equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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