Asymptotic models for free boundary flow in porous media
arXiv:1810.10756 · doi:10.1016/j.physd.2019.02.013
Abstract
We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to be very small. The models we derive capture the nonlinear interaction of the original free boundary Darcy and Forchheimer problem up to quadratic terms. Furthermore, we provide models that consider both the two-dimensional and three-dimensional cases, with and without bottom topography.
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- On the motion of gravity-capillary waves with odd viscosity
- Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
- Well-posedness of an asymptotic model for free boundary Darcy flow in porous media in the critical Sobolev space
- Global well-posedness and decay for viscous water wave models