Global weak solutions to the compressible quantum Navier-Stokes equation and its semi-classical limit

被引：39

作者：

Lacroix -Violet, Ingrid ^{[1
]}

Vasseur, Alexis ^{[2
]}

机构：

[1] Univ Lille 1, INRIA RAPSODI Team, Lab Paul Painleve, Lille, France

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 114卷

关键词：

Global weak solutions; Compressible quantum; Navier Stokes equations; Vacuum; Degenerate viscosity; EXISTENCE;

D O I：

10.1016/j.matpur.2017.12.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerate viscosity, together with the lack of integrability on the velocity. Our method is based on the construction of weak solutions that are renormalized in the velocity variable. The existence, and stability of these solutions do not need the Mellet-Vasseur inequality. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：191 / 210

页数：20

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