Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains

Abstract

<p style='text-indent:20px;'>For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the uniqueness of a solution is related to the existence of a regular solution. They may be obtained under suitable assumptions on the data and smoothness assumptions on the domain (at least <inline-formula><tex-math id="M1">\begin{document}$ C^{2,1} $\end{document}</tex-math></inline-formula>). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely <i>Lipschitz domains</i> of physical interest, that we call <i>sectors</i>.</p>