Christian Rohde

Weak-strong uniqueness and relaxation limit for a Navier–Stokes–Korteweg model

We consider a parabolic relaxation model for the compressible Navier-Stokes-Korteweg equations in the isothermal framework. This system depends on the relaxation parameters $α,β>0$ and approximates formally solutions of the compressible Navier-Stokes-Korteweg equations in the rel...

On Hyperbolic Approximations for a Class of Dispersive and Diffusive-Dispersive Equations

Abstract We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth solutions is achieved by constru...

A Hyperbolic Model for Two-Layer Thin Film Flow with a Perfectly Soluble Anti-Surfactant

Abstract. We consider the motion of a two-layer thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial stress driving a Marangoni-type...