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A removable singularity in a suitable weak solution to the Navier-Stokes equations. (English) Zbl 1245.35085

Summary: We formulate a new criterion for regularity of a suitable weak solution \(v\) to the Navier-Stokes equations at the point \((x_{0}, t_{0})\). We show that it is sufficient to impose conditions on the Serrin-type integrability of \(v\) and the associated pressure \(p\) in a parabolic neighbourhood of \((x_{0}, t_{0})\), intersected with the exterior of a certain space-time paraboloid with the vertex at point \((x_{0}, t_{0})\). We make no special assumptions on \(v\) or \(p\) in the interior of the paraboloid.

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35D30 Weak solutions to PDEs
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