期刊
MATHEMATISCHE ZEITSCHRIFT
卷 242, 期 2, 页码 251-278出版社
SPRINGER-VERLAG
DOI: 10.1007/s002090100332
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We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brozis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in R-n and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces.
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