Global well-posedness of the one-phase Muskat problem with surface tension

The one-phase Muskat problem models the boundary between wet and dry regions in a porous material under Darcy’s law. Including surface tension is physically important but makes the analysis more difficult. Hyunwoo Kwon presents a proof of global well-posedness for small initial data in the subcritical regime, together with convergence of the solution to zero in Lipschitz norm at long times. The work is presented as the first global well-posedness result for this version of the problem with surface tension. Time permitting, the talk also includes a numerical experiment. The research is joint with Hongjie Dong.