REGULARITY FOR THE 3D EVOLUTION NAVIER-STOKES EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS IN SOME LIPSCHITZ DOMAINS

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 C-2,C-1). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest, that we call sectors.

Automated summary

For the evolution of Navier-Stokes equations in bounded 3D domains, the uniqueness of the solution is determined by the existence of a regular solution. Under appropriate assumptions on the data and smoothness assumptions on the domain, this uniqueness can be obtained. Using a symmetrization technique, we prove these results for the case of Navier boundary conditions in a class of merely Lipschitz domains called sectors.