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Zbl 1055.35087
Kozono, Hideo; Ogawa, Takayoshi; Taniuchi, Yasushi
The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. (English)
[J] Math. Z. 242, No. 2, 251-278 (2002). ISSN 0025-5874; ISSN 1432-1823/e

The authors give critical Sobolev inequalities in Besov spaces with logarithmic form similar to those of Brezis-Gallouet-Wainger and Beale-Kato-Majda. Applications to the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations and the gradient flow to the harmonic map to the sphere are discussed.
[B. G. Pachpatte (Aurangabad)]

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
35Q05 Euler-Poisson-Darboux equation and generalizations
35L60 First-order nonlinear hyperbolic equations
76B03 Existence, uniqueness, and regularity theory
76D03 Existence, uniqueness, and regularity theory

Keywords: regularity; Navier-Stokes equations; Euler equations; gradient flow; harmonic map

Cited in: Zbl 1186.42013

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