Kozono, Hideo; Ogawa, Takayoshi; Taniuchi, Yasushi The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. (English) Zbl 1055.35087 Math. Z. 242, No. 2, 251-278 (2002). 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. Reviewer: B. G. Pachpatte (Aurangabad) Cited in 1 ReviewCited in 200 Documents MSC: 35Q30 Navier-Stokes equations 35Q05 Euler-Poisson-Darboux equations 35L60 First-order nonlinear hyperbolic equations 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids Keywords:regularity; Navier-Stokes equations; Euler equations; gradient flow; harmonic map PDFBibTeX XMLCite \textit{H. Kozono} et al., Math. Z. 242, No. 2, 251--278 (2002; Zbl 1055.35087) Full Text: DOI