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Wellposedness of the two and three dimensional full water wave problem

Tuesday, February 23, 2010 - 11:30am - 12:15pm
EE/CS 3-180
Sijue Wu (University of Michigan)
Keywords: water wave problem

Abstract: We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.

MSC Code: 
76B15
Keywords: