Juliana Honda

Universidade Estadual de Maringá, Brazil

Title: Local strong solution for a nonhomogeneous incompressible cell-fluid Navier-Stokes model with chemotaxis

Abstract: This work addresses a general nonhomogeneous incompressible cell-fluid Navier-Stokes model incorporating chemotaxis in a two or three-dimensional bounded domain. This model comprises two mass balance equations and two general momentum balance equations, specifically for the cell and fluid phases, combined with a convection-diffusion-reaction equation for oxygen. We establish the existence and uniqueness of a local strong solution under initial data that satisfy natural compatibility conditions. Additionally, we present a blow-up criterion for the strong solution.