A 2D fluid-based model for individual cell crawling.

This paper presents the analysis and numerical simulations of a two-dimensional model of single-cell crawling migration, focusing on intracellular dynamics. The fluid-based model relies on the interaction between the actin cytoskeleton and a generic molecular regulator of its activity. The model is formulated as a Poisson problem with Darcy's law, coupled with a nonlocal advection-diffusion equation for the molecular concentration, where the non-local term involves boundary values. Existence and uniqueness of resting and travelling stationary states are established in certain parameter domains, along with linear stability in the resting case. Numerical simulations illustrate both cell regimes. This demonstrates the model's ability to capture key features of cell migration.