Global well-posedness for the 2D one-phase Muskat equations

I will present a recent result jointly with Francisco Gancedo (Universidad de Sevilla) and Huy Q. Nguyen (University of Maryland), in which we obtained the global well-posedness for the 2D one-phase Muskat problem with arbitrary large Lipschitz initial data. The equation arises from a free boundary problem for a 2D fluid filtered in porous media.