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Well-posedness for the equations of motion of an incompressible, inviscid, self-gravitating fluid with free boundary
PDE Seminar| Speaker: | Hakan Nordgren, UCSD |
| Location: | 3106 MSB |
| Start time: | Fri, Nov 9 2007, 4:10PM |
Description
We describe a methodology developed by Daniel Coutand and Steve Shkoller by
using it to prove that the equations of motion of an incompressible,
inviscid, self-gravitating fluid with free boundary are well-posed. The
methodology consists of the use of a smoothing operator which smoothes
along the boundary of the fluid. This then allows the use of a
fixed-point-type argument, which provides a solution to a smoothed version
of the problem. Estimates subsequently show that these solutions converge
to a solution of the full problem.