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arXiv · 1004.3975

Singularity Formation in a Surface Wave Model

Angel Castro·Diego Cordoba·Francisco Gancedo
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Abstract

In this paper we study the Burgers equation with a nonlocal term of the form $Hu$ where $H$ is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch. We prove blow up in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form $Λ^αHu$ for $0<α< 1$, finite time singularity formation is also shown.

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Angel Castro, Diego Cordoba, Francisco Gancedo. 2010-04-22. Singularity Formation in a Surface Wave Model. https://doi.org/10.1088/0951-7715%2F23%2F11%2F006

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