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arXiv:1004.4287 [math.FA]Abstract References Reviews Resources

Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations

Hichem Hajaiej, Luc Molinet, Tohru Ozawa, Baoxiang Wang

Published 2010-04-24, updated 2011-01-26Version 3

Sufficient and necessary conditions for the generalized Gagliardo-Nirenberg (GN) inequality in Besov spaces and Triebel-Lizorkin spaces are obtained. Applying the GN inequality, we show that the finite-time blowup solutions have concentration phenomena in critical Lebesgue space L^3. Moreover, we consider the minimizer for a class of variational problem by applying the fractional GN inequality.

Comments: 40 Pages

Categories: math.FA, math.AP

Subjects: 42B35, 46E35, 35J50, 35Q40, 47J30

Keywords: fractional gagliardo-nirenberg inequalities, generalized boson equations, necessary conditions, sufficient, applications

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