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Spreading of the Free Boundary of an Ideal Fluid in a Vacuum

PDE and Applied Math Seminar

Speaker: Thomas Sideris, UC Santa Barbara
Location: 1147 MSB
Start time: Fri, Nov 9 2012, 3:10PM

Consider an ideal fluid occupying a bounded region in space surrounded by vacuum. The boundary of this region is free to move with the fluid. We shall show under the assumptions of positive density and pressure that the diameter of this region grows at least linearly in time as long as the fluid motion remains $C^1$. The linear spreading rate is illustrated with an explicit family of spherically symmetric compressible solutions.