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Mostrando ítems 31-37 de 37
Artículo
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
(Princeton University, 2012)
The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor ...
Artículo
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
(National Academy of Sciences (United States), 2014)
In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the “splash singularity” blow-up scenario; in other words, we prove that the contours evolving from either of ...
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Artículo
Global regularity of 2D density patches for inhomogeneous Navier-Stokes
(Springer, 2018)
This paper is about Lions’ open problem on density patches: whether inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev ...
Artículo
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
(Springer, 2007-07)
We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase ...
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.
Artículo
Finite time singularities for the free boundary incompressible Euler equations
(Princeton University, 2013)
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the ...