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

2010/04/24 by Hichem Hajaiej, Hajaiej, Hichem, Luc Molinet +5 · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP #math.FA #msc:35J50 #msc:35Q40 #msc:42B35 #msc:46E35 #msc:47J30

paper · pdf · doi:10.48550/arxiv.1004.4287

40 Pages

arxiv created 2011/01/26 · arxiv updated 2011/01/27

Abstract

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 L³. Moreover, we consider the minimizer for a class of variational problem by applying the fractional GN inequality.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

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