Convergence rate for the incompressible limit of nonlinear diffusion–advection equations

The incompressible limit of nonlinear diffusion equations porous medium type has attracted a lot attention in recent years, due to its ability link the weak formulation cell-population models free boundary problems Hele-Shaw type. Although vast literature is available on this singular limit, little known convergence rate solutions. In work, we compute negative Sobolev norm and, upon interpolating with BV-uniform bounds, deduce appropriate Lebesgue spaces.