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Interior regularity criterion via pressure on weak solutions to the Navier–Stokes equations
Author(s) -
Suzuki Tomoyuki
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410476
Subject(s) - mathematics , bounded function , gravitational singularity , navier–stokes equations , scaling , domain (mathematical analysis) , class (philosophy) , mathematical analysis , geometry , compressibility , mechanics , physics , computer science , artificial intelligence
Abstract Consider the nonstationary Navier–Stokes equations in Ω × (0, T ), where Ω is a bounded domain in ℝ 3 . We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it possible to obtain better information around the singularities. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)