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Artículo
Interface evolution: the Hele-Shaw and Muskat problems
(Princeton University, 2011)
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy’s law. The free boundary is given by the discontinuity among the densities and viscosities of ...
Artículo
Turning waves and breakdown for incompressible flows
(National Academy of Sciences, 2011-03-22)
We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial ...
Artículo
Lack of uniqueness for weak solutions of the incompressible porous media equation
(Springer, 2011-06)
In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz´ekelyhidi we prove non-uniqueness for solutions in L∞ in space and time.