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.