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 …

The existence of global-in-time weak solutions to the one-dimensional viscous quantum
hydrodynamic equations is proved. The model consists of the conservation laws for the …

In this paper, we establish a new blow-up criterion of the strong solution to the quantum
hydrodynamic model. This blow-up criterion is different from the one established in our …

In this study, we consider the large time behavior of the solution to the one-dimensional
isentropic compressible quantum Navier–Stokes–Poisson equations. The system describes …

In this paper we firstly investigate the local-in-time existence of smooth solution for the
quantum hydrodynamic models (QHD) in R d. Then we prove that any smooth solution of the …

In this article, we focus on the short time strong solution to a compressible quantum
hydrodynamic model. We establish a blow-up criterion about the solutions of the …

We give an overview of analytic investigations of quantum semiconductor models, where we
focus our attention on two classes of models: quantum drift diffusion models, and quantum …

In this paper, we prove that any smooth solutions of quantum hydrodynamic model which
satisfies suitable conditions will blow up in finite time in half space. This model can be …

Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model -
Zhang - 2022 - Mathematical Methods in the Applied Sciences - Wiley Online Library Skip to …

The quantum hydrodynamic phenomenon comes from superfluid, superconductor,
semiconductor and so on. As it's well known, semiconductor is a kind of material whose …