University of Cambridge > Talks.cam > 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 Partial Differential Equations seminar series.

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