Large-time existence of surface waves in incompressible viscous fluids with or without surface tension (Q1898383)

The motion of a viscous incompressible fluid in a three-dimensional domain such as an ocean of infinite extent and finite depth is considered. To this end, the viscosity \(\nu\) and the surface tension \(\sigma\) are taken to be constant. The existence of temporally global structures is then established systematically for both cases \(\sigma > 0\) and \(\sigma = 0\).