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

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 L^3. Moreover, we consider the minimizer for a class of variational problem by applying the fractional GN inequality.

arXiv comment40 Pages

References in corpus (2)

• Fractional dynamics of systems with long-range interaction
• A weak-strong convergence property and symmetry of minimizers of constrained variational problems in ${\mathbb{R}}^N$

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