Special Session 111: Evolution Equations and Operator Semigroups: Theory and Applications

Two-Dimensional Keller-Segel-Navier-Stokes System of Potential Type
Gabriela Planas
Universidade Estadual de Campinas
Brazil
Co-Author(s):    D. Barbosa (Brazil) and F. Guill\`en-Gonz\`alez (Spain)
Abstract:
In this talk, we study a Keller-Segel-Navier-Stokes system posed on a two-dimensional domain, describing the interaction of a cell density with two chemical signals: an attractive signal that is consumed by the cells and a repulsive signal that is produced by them. The model incorporates general consumption and production rates together with a generalized logistic growth law for the cell population. We impose no-flux boundary conditions on the cell density and chemical concentrations, along with Dirichlet boundary conditions for the fluid velocity field. Under suitable conditions linking the chemotactic sensitivities, attraction and consumption rates, and the strength of logistic competition, we prove the existence of global classical solutions to the system.