On regularity and singularity for L(0 , T; L3 , w(R3)) solutions to the Navier–Stokes equations

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We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L(0 , T; L3 , w(R3)) without any smallness assumption on that scale, where L3 , w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.

Original languageEnglish
Pages (from-to)617-642
Number of pages26
JournalMathematische Annalen
Issue number1-2
Publication statusPublished - 2020 Jun 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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