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Math Colloquium
Ian Tice
Universite Paris-Est Creteil
Title: Global well-posedness and decay for the viscous surface wave problem without surface tension

Abstract: We study the incompressible, gravity-driven Navier-Stokes equations in three dimensional domains with free upper boundaries and fixed lower boundaries, in both the horizontally periodic and non-periodic settings. The effect of surface tension is not included. We employ a novel two-tier nonlinear energy method that couples the boundedness of certain high-regularity norms to the algebraic decay of lower-regularity norms. The algebraic decay allows us to balance the growth of the highest order derivatives of the free surface function, which then allows us to derive a priori estimates for solutions. When coupled with an appropriate local well-posedness theory, our a priori estimates then yield global-in-time solutions that decay to equilibrium at an algebraic rate. This is joint work with Yan Guo.

Date: Tuesday, December 13, 2011
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Fonseca
Note: Refreshments 4:00 pm, Wean Hall 6220