A non-local porous media equation
Luis A. Caffarelli, Maria Pia Gualdani, Nicola Zamponi · arXiv (Cornell University) · 2018
In this manuscript we consider a non-local porous medium equation with non-local diffusion effects given by a fractional heat operator $\partial_t + (-\Delta)^s$ in three space dimensions for $3/4\le s\le 1$. Global in time existence of weak solutions is shown by employing a time semi-discretization of the equations, an energy inequality and a uniform estimate for the first moment of the solution to the discretized problem.