Global Solvability in a Two-Species Keller-Segel-Navier-Stokes System with Sub-Logistic Source

Abstract

This paper is concerned with a two-species Keller-Segel-Navier-Stokes model with sub-logistic source in a bounded domain with smooth boundary under no-flux/no-flux/no-flux/Dirichlet boundary conditions. For a large class of cell kinetics including sub-logistic degradation, it is shown that under an explicit condition involving the chemotactic strength and initial mass of cells, the two-dimensional Keller-Segel-Navier-Stokes problem possesses a global and bounded classical solution. In the case with arbitrary superlinear logistic degradation, it is proved that for all suitably regular initial data, the two-dimensional Keller-Segel-Navier-Stokes problem has at least one globally defined solution in an appropriate generalized sense. These results improves and extends the previously known ones.

Keywords

Keller-Segel-Navier-Stokes / sub-logistic source / boundedness / generalized solution