Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system
Michael Winkler
Universität Paderborn, Paderborn, Germany
Abstract
A family of interpolation inequalities is derived, which differ from estimates of classical Gagliardo–Nirenberg type through the appearance of certain logarithmic deviations from standard Lebesgue norms in zero-order expressions. Optimality of the obtained inequalities is shown. A subsequent application reveals that when posed under homogeneous Neumann boundary conditions in smoothly bounded planar domains and with suitably regular initial data, for any choice of the Keller–Segel-type migration–consumption system , , admits a global classical solution.
Cite this article
Michael Winkler, Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first
DOI 10.4171/AIHPC/141