Well-posedness of an asymptotic model for free boundary Darcy flow in porous media in the critical Sobolev space

Abstract

We prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow is well posed in ${\dot{H}}^{3/2}$, and globally well-posed if the initial datum is small in ${\dot{H}}^{3/2}$.

7 pages, comments are welcome

References in corpus (1)

• Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space