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Mostrando ítems 1-4 de 4
Artículo
Generalized surface quasi-geostrophic equations with singular velocities
(Wiley, 2012)
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized ...
Artículo
Splash singularity for water waves
(National Academy of Sciences, 2012-01-17)
We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical ...
Artículo
Finite time singularities for water waves with surface tension
(AIP Publishing, 2012-11)
Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself ...
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 ...