##### Department of Mathematics,

University of California San Diego

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### Math 248 - Real Analysis Seminar

## Hakan Nordgren

#### UCSD Graduate student

## Well-posedness for the equations of motion of an incompressible, inviscid, self-gravitating fluid with free boundary

##### Abstract:

Building on work by Hans Lindblad, Daniel Coutand and Steve Shkoller, we 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.

### November 27, 2007

### 9:00 AM

### AP&M 6218

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