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Publication 18-CNA-015
Antoine Remond-Tiedrez Ian Tice Abstract: We study a three-dimensional incompressible viscous
fluid in a horizontally periodic domain
with finite depth whose free boundary is the graph of a function. The
fluid is subject to gravity and
generalized forces arising from a surface energy. The surface energy incorporates both bending and surface
tension effects. We prove that for initial conditions sufficiently close to equilibrium the problem is globally
well-posed and solutions decay to equilibrium exponentially fast, in an appropriate norm. Our proof is
centered around a nonlinear energy method that is coupled to careful estimates of the fully nonlinear surface
energy.Get the paper in its entirety as 18-CNA-015.pdf |