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
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1004.4287

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

Related

• Gagliardo-Nirenberg type inequalities using fractional Sobolev spaces and Besov spaces
• Gagliardo-Nirenberg Inequalities in Fractional Coulomb-Sobolev spaces for Radial functions
• Gagliardo-Nirenberg inequality in anisotropic Lebesgue spaces and energy equality in the Navier-Stokes equations
• Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces
• Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces