2018/06/20 by Remond-Tiedrez, Antoine, Tice, Ian
#35Q30 #35R35 #74F10 (Secondary) #74K15 #76D45 #76E17 (Primary) 35B40 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1806.07660
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.