On steady waves in two-layer fluids and ferrofluids

Abstract: This thesis concerns travelling waves in a two-layer fluid and on a ferrofluid jet. We prove existence of several types of such waves by reformulating the corresponding governing equation as an infinite dimensional dynamical system, where an unbounded spatial coordinate is used as time. A center-manifold reduction is then employed to reduce the system to a locally equivalent finite dimensional system, which can be further studied using dynamical systems methods. We also prove the existence of solitary wave solutions to a modified class of Green-Naghdi equations. This is an equation involving non-local operators which can be used to model waves in a two-layer fluid. We find solitary wave solutions by identifying them as solutions of a constrained minimization problem, and then proving existence of such minimizers.