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Spreading of the Free Boundary of an Ideal Fluid in a VacuumPDE 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.