Local boundary regularity for the Navier-Stokes equations in nonendpoint borderline Lorentz spaces

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Abstract

Local regularity up to the flat part of the boundary is proved for certain classes of distributional solutions that are L∞L3,q with q finite. The corresponding result for the interior case was recently proved by Wang and Zhang, see also Phuc’s paper. For local regularity up to the flat part of the boundary, q = 3 was established by G. A. Seregin. Our result can be viewed as an extension of it to L3,q with q finite. New scale-invariant bounds, refined pressure decay estimates near the boundary and development of a convenient new ϵ-regularity criterion, are central themes in providing this extension.
Original languageEnglish
Pages (from-to)391–413
JournalJournal of Mathematical Sciences N.Y.
Volume224
Issue number3
DOIs
Publication statusPublished - 5 Jun 2017

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