We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is
The problem is posed in with nonnegative initial data that are integrable and decay at infinity. A previous paper has established the existence of mass-preserving, nonnegative weak solutions satisfying energy estimates and finite propagation. As main results we establish the boundedness and regularity of such weak solutions. Finally, we extend the existence theory to all nonnegative and integrable initial data.
Cite this article
Luis A. Caffarelli, Fernando Soria, Juan Luis Vázquez, Regularity of solutions of the fractional porous medium flow. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1701–1746DOI 10.4171/JEMS/401