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

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  • 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^{2,1} $). 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.

    Mathematics Subject Classification: 35Q30, 35K20.


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  • Figure 1.  From left to right: a pipe bifurcation, a joint, a vein, a drop, a tunnel, a bottle

    Figure 2.  Some sectors obtained as subdomains of a sphere

    Figure 3.  Some Lipschitz domains that are not sectors, according to Definition 3

    Figure 4.  Sectors of type $ (B) $

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