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

TL;DR

This paper proves the existence of stationary internal waves in a 2D aquarium with low viscosity, using complex deformation techniques under specific dynamical assumptions.

Contribution

It introduces a novel method employing complex deformations to establish invertibility of the internal wave operator with small viscosity.

Findings

Uniform solvability of the stationary internal wave problem

Invertibility of the inviscid operator via complex deformation

Applicability under Morse--Smale dynamical conditions

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.