Madelung, Gross--Pitaevskii and Korteweg Page 1 Nonlinearity PAPER Madelung, Gross–Pitaevskii
and Korteweg To cite this article: Rémi Carles et al 2012 Nonlinearity 25 2843 View the …

Even though the Madelung equations are central to many'classical'approaches to the
foundations of quantum mechanics such as Bohmian and stochastic mechanics, no …

Semiconductor devices are ubiquitous in the modern computer and telecommunications
industry. A precise knowledge of the transport equations for electron flow in semiconductors …

The global-in-time existence of weak solutions to the barotropic compressible quantum
Navier–Stokes equations in a three-dimensional torus for large data is proved. The model …

In this paper, the main objective is to generalize to the Navier–Stokes–Korteweg (with
density dependent viscosities satisfying the BD relation) and Euler–Korteweg systems a …

We consider the Schrödinger equation with a logarithmic nonlinearity in a dispersive regime.
We show that the presence of the nonlinearity affects the large time behavior of the solution …

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 …

In this paper we study global existence of weak solutions for the quantum hydrodynamics
system in two-dimensional energy space. We do not require any additional regularity and/or …

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 consider the Quantum Navier–Stokes system both in two and in three space
dimensions and prove the global existence of finite energy weak solutions for large initial …