Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

Abstract

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.

19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phys

References in corpus (1)

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

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• Thermodynamic and vortic fine structures of real Schur flows
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