In this paper we present a novel first order hyperbolic reformulation of the barotropic Navier-
Stokes-Korteweg system. The new formulation is based on a combination of the first order …

This work is devoted to proving existence of global weak solutions for a general isothermal
model of capillary fluids derived by Dunn and Serrin (Arch Rational Mech Anal 88 (2): 95 …

The Euler-Korteweg model results from a modification of the standard Euler equations
governing the motion of compressible inviscid fluids through the adjunction of the Korteweg …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

We consider a Euler system with dynamics generated by a potential energy functional. We
propose a form for the relative energy that exploits the variational structure and we derive a …

In this paper, we present a new explicit second-order accurate structure-preserving finite
volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg …

A compressible Cahn-Hilliard fluid model is derived from the kinetic theory of dense gas
mixtures. The fluid model involves a van der Waals and Cahn-Hilliard gradient energy, a …

Abstract The Euler–Korteweg equations are a modification of the Euler equations that take
into account capillary effects. In the general case they form a quasi-linear system that can be …

We study the defocusing nonlinear Schrödinger (NLS) equation written in hydrodynamic
form through the Madelung transform. From the mathematical point of view, the …

We present a family of relaxation models for thin films flows where both viscosity and surface
tension effects are inherent. In a first step, a first-order hyperbolic approximation to the …