Global analysis of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain

Guochun Wu; Yinghui Zhang

doi:10.3934/dcdsb.2018157

Article Contents

2018, Volume 23, Issue 4: 1411-1429. Doi: 10.3934/dcdsb.2018157

This issue Previous Article Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model Next Article A time-delay in the activator kinetics enhances the stability of a spike solution to the gierer-meinhardt model

Global analysis of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain

Guochun Wu^1, and
Yinghui Zhang^2, ,

1.
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
2.
Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China

* Corresponding author: Yinghui Zhang
* Corresponding author: Yinghui Zhang

Received: November 2016

Revised: March 2018

Early access: April 16, 2018

Published online: April 16, 2018

The first author is supported by National Natural Science Foundation of China #11701193, #11671086. The second author is supported by Hunan Provincial Natural Science Foundation of China #2017JJ2105, and National Natural Science Foundation of China #11571280, #11771150, #11301172, 11226170, and National Scholarship Fund in Hunan province cooperation projects.

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Abstract

In this paper, we investigate global existence and asymptotic behavior of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain with no-slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in $H^2(Ω)$ . Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

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Mathematics Subject Classification: Primary: 76W05, 35Q35; Secondary: 35D05.

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