Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system

  • Michael Winkler

    Universität Paderborn, Paderborn, Germany
Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system cover
Download PDF

A subscription is required to access this article.

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