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Plenary Lecture 10: Absence of the interface splash singularity for the two-fluid Euler equations

Shkoller, S (University of Oxford)
Friday 27 June 2014, 09:00-09:45

Seminar Room 1, Newton Institute


An interface splash singularity occurs when a locally smooth fluid interface self-intersects. Such interface singularities occur for one-fluid interfaces in the Euler equations and other fluids models.

By means of elementary arguments in Lagrangian coordinates, we prove that such a singularity cannot occur in finite-time for a two-fluid interface evolved by either the incompressible Euler equations (with surface tension) or the Muskat equations. By assuming that such a singularity can occur, we find a sharp blow-up rate for the vorticity, and characterize the geometry of the evolving interface. This leads to a contradiction, showing that such a singularity can occur. This is joint work with D. Coutand.


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