Article
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
Author/s | Gancedo García, Francisco
Strain, Robert M. |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2014 |
Deposit Date | 2016-09-09 |
Published in |
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Abstract | 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 ... 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 these systems cannot intersect at a single point while the free boundary remains smooth. Splash singularities have been shown to hold for the free boundary incompressible Euler equation in the form of the water waves contour evolution problem. Our result confirms the numerical simulations in earlier work, in which it was shown that the curvature blows up because the contours collapse at a point. Here, we prove that maintaining control of the curvature will remove the possibility of pointwise interphase collapse. Another conclusion that we provide is a better understanding of earlier work in which squirt singularities are ruled out; in this case, a positive volume of fluid between the contours cannot be ejected in finite time. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España National Science Foundation (NSF). United States |
Project ID. | MTM2011-26696
DMS-1200747 |
Citation | Gancedo García, F. y Strain, R.M. (2014). Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem. Proceedings of the National Academy of Sciences, 111 (2), 635-639. |
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