On the Incompressible Limit for a Tumour Growth Model Incorporating Convective Effects
In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quir´os, and V´azquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of nutrients, oxygen, or, possibly, as a result of self-propulsion. The main result of this work is the incompressible limit of this model which builds a bridge between the density-based model and a geometry free-boundary problem by passing to a singular limit in the pressure law. The limiting objects are then proven to be unique.