Boundary partial regularity for the high dimensional Navier-Stokes equations

Abstract

We consider suitable weak solutions of the incompressible Navier--Stokes equations in two cases: the 4D time-dependent case and the 6D stationary case. We prove that up to the boundary, the two-dimensional Hausdorff measure of the set of singular points is equal to zero in both cases.

Revision, 28 Pages, to appear in J. Funct. Anal

References in corpus (1)

• Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

Cited by in corpus (7)

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• Local $\epsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations
• Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary
• Boundary $\epsilon$-regularity criteria for the 3D Navier-Stokes equations
• Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations