Small Internal waves in porous media do not break

What is it about?

In this paper we study the dynamics of an internal wave between two different incompressible fluids in a confined porous medium and show that if the initial wave satisfies certain size conditions involving amplitude and slope, the wave never breaks and exists for every positive time.

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Photo by Abbie Bernet on Unsplash

Photo by Abbie Bernet on Unsplash

Why is it important?

Besides being the first global existence of weak solution for the so called confined Muskat problem, it also shows that the bounded domain (when the seabed is present) is more singular than the unbounded case (when only deep water is considered).