David Ambrose
Free-Surface Problems in Irrotational 3D Fluids

We consider three particular free-surface flows in irrotational 3D fluids; they are the vortex sheet with surface tension, the water wave, and Darcy flow.  We describe a common framework in which the equations of motion for each problem can be formulated.  This involves choosing a favorable parameterization of the free surface and convenient dependent variables.  After the problems have been formulated in this manner, energy estimates are possible.  Well-posedness of the initial value problem in each case follows from the energy estimates.


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