A New Criterion for Partial Regularity of Suitable Weak Solutions to the Navier-Stokes Equations

JÖrg Wolf ()
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JÖrg Wolf: Mathematical Institute, Humboldt University Berlin

A chapter in Advances in Mathematical Fluid Mechanics, 2009, pp 613-630 from Springer

Abstract: Abstract In the present paper we study local properties of suitable weak solutions to the Navier-Stokes equation in a cylinder Q = Ω × (0, T). Using the local representation of the pressure we are able to define a positive constant ɛ⋆ such that for every parabolic subcylinder QR ⊂ Q the condition $$R^{-2}\int_{Q_R}|u|^3dxdt\leq\varepsilon_{\ast}$$ implies $${\bf U}\in L^{\infty}(Q_{R/2})$$ ). As one can easily check this condition is weaker then the well known Serrin's condition as well as the condition introduced by Farwig, Kozono and Sohr in a recent paper. Since our condition can be verified for suitable weak solutions to the Navier-Stokes system it improves the known results substantially.

Keywords: Navier-Stokes equations; Partial regularity; Local regularity (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04068-9_34

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DOI: 10.1007/978-3-642-04068-9_34

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