Mathematics Colloquia and Seminars

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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.