Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity

Guangwu Wang; Boling Guo

doi:10.3934/dcdsb.2019133

Article Contents

2019, Volume 24, Issue 11: 6141-6166. Doi: 10.3934/dcdsb.2019133

This issue Previous Article A Max-Cut approximation using a graph based MBO scheme Next Article Linearized stability for abstract functional differential equations subject to state-dependent delays with applications

Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity

Guangwu Wang^1, , and
Boling Guo^2,

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing, 100088, China

^* Corresponding author: Guangwu Wang
^* Corresponding author: Guangwu Wang

Received: December 2017

Early access: July 2019

Published: August 2019

The first author is supported by the National Natural Science Foundation of China No. 11801107, and the second author is supported by the National Natural Science Foundation of China No. 11731014

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Abstract

In this paper we investigate the global existence of the weak solutions to the quantum Navier-Stokes-Landau-Lifshitz equations with density dependent viscosity in two dimensional case. We research the model with singular pressure and the dispersive term. The main technique is using the uniform energy estimates and B-D entropy estimates to prove the convergence of the solutions to the approximate system. We also use some convergent theorems in Sobolev space.

Keywords:

Navier-Stokes-Landau-Lifshitz equations,
global weak solutions,
energy estimate,
B-D entropy estimate.

Mathematics Subject Classification: Primary: 35A01, 35D30, 35M31, 35Q40; Secondary: 76N10.

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