On regularity criteria in conjunction with the pressure of the Navier-Stokes equations

Kyungkeun Kang, Jihoon Lee

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10 Citations (Scopus)

Abstract

We present new regularity criteria involving the integrability of the pressure for the Navier-Stokes equations in bounded domains with smooth boundaries.We prove that either if the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 3/2<γ≤∞ or if the gradient of the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 1<γ≤∞, then weak solutions are regular. Local regularity criteria in terms of pressure are also established near a flat boundary as well as in the interior for suitable weak solutions.

Original languageEnglish
Article number80762
JournalInternational Mathematics Research Notices
Volume2006
DOIs
Publication statusPublished - 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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