Self-Similarity in a Thin Film Muskat Problem

[hal-00636647, v1] A gradient flow approach to a thin film approximation of the Muskat problem

Abstract. A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two ...

A gradient flow approach to a thin film approximation of the Muskat problem

A thin film approximation of the Muskat problem with gravity and capillary forces

Abstract. Existence of nonnegative weak solutions is shown for a thin film approximation of the Muskat problem with gravity and capillary forces taken into account. The model describes the space-time evolution of the heights of the two fluid layers and is a fully coupled system of two fourth order degenerate parabolic equations. The existence proof relies on the fact that this system can be vie...

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.

Self-powered thin-film motion vector sensor

Harnessing random micromeso-scale ambient energy is not only clean and sustainable, but it also enables self-powered sensors and devices to be realized. Here we report a robust and self-powered kinematic vector sensor fabricated using highly pliable organic films that can be bent to spread over curved and uneven surfaces. The device derives its operational energy from a close-proximity triboele...