Stationary internal waves in a two-dimensional aquarium at low viscosity

Abstract

We prove the uniform solvability of a stationary problem associated to internal waves equation with small viscosity in a two dimensional aquarium with real-analytic boundary, under a Morse--Smale dynamical assumption. This is achieved by using complex deformations of the aquarium, on which the inviscid stationary internal wave operator is invertible.

arXiv comment56 pages, 3 figures. Comments are welcome!