Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space. (August 2021) - Scrobogna, Stefano
Abstract: We prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow, derived in Granero-Belinchón and Scrobogna (2019), is well posed in H ̇ 3 ∕ 2 S 1, and globally well-posed if the initial datum is small in H ̇ 3 ∕ 2 S 1 .