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Global existence and asymptotic behavior of affine solutions to the free boundary Euler equations in 3d

PDE and Applied Math Seminar

Speaker: Thomas Sideris, UC Santa Barbara
Location: 1147 MSB
Start time: Fri, Apr 29 2016, 4:10PM

We consider the initial free boundary value problem for the motion of ideal fluids surrounded by vacuum in 3d. In the special case of affine motion, the partial differential equations reduce to a globally solvable system of nonlinear ordinary differential equations. The evolving fluid domain is a rotating ellipsoid whose diameter grows at a rate proportional to time. After rescaling, we find that 1 or 2 of the major axes may degenerate, as time tends to infinity.