Derivation and analysis of a Stokes-transport system in evolving vessels modeling thermoregulation in human skin

We consider a Stokes flow coupled with advective-diffusive transport in an evolving domain with boundary conditions allowing for inflow and outflow. The evolution of the domain is induced by the transport process, leading to a fully coupled problem. Our aim is to model the thermal control of blood flow in human skin. To this end, the model takes into account the temperature-dependent production of biochemical substances, the subsequent dilation and constriction of blood vessels, and the resulting changes in convective heat transfer. We prove existence and uniqueness of weak solutions using a fixed point method that allows us to treat the nonlinear coupling.