University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Global well-posedness and decay for the viscous surface wave problem without surface tension

Global well-posedness and decay for the viscous surface wave problem without surface tension

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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.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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