# Decay of the 3D viscous liquid-gas two-phase flow model with damping

## Abstract

We establish the optimal L{sup p} − L{sup 2}(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, L{sup p} − L{sup 2} estimates for the linearized equations, and delicate energy estimates.

- Authors:

- Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006 (China)

- Publication Date:

- OSTI Identifier:
- 22596443

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; DAMPING; DECAY; FLOW MODELS; MATHEMATICAL SOLUTIONS; THREE-DIMENSIONAL CALCULATIONS; TWO-PHASE FLOW

### Citation Formats

```
Zhang, Yinghui, E-mail: zhangyinghui0910@126.com.
```*Decay of the 3D viscous liquid-gas two-phase flow model with damping*. United States: N. p., 2016.
Web. doi:10.1063/1.4961319.

```
Zhang, Yinghui, E-mail: zhangyinghui0910@126.com.
```*Decay of the 3D viscous liquid-gas two-phase flow model with damping*. United States. doi:10.1063/1.4961319.

```
Zhang, Yinghui, E-mail: zhangyinghui0910@126.com. Mon .
"Decay of the 3D viscous liquid-gas two-phase flow model with damping". United States.
doi:10.1063/1.4961319.
```

```
@article{osti_22596443,
```

title = {Decay of the 3D viscous liquid-gas two-phase flow model with damping},

author = {Zhang, Yinghui, E-mail: zhangyinghui0910@126.com},

abstractNote = {We establish the optimal L{sup p} − L{sup 2}(1 ≤ p < 6/5) time decay rates of the solution to the Cauchy problem for the 3D viscous liquid-gas two-phase flow model with damping and analyse the influences of the damping on the qualitative behaviors of solution. It is observed that the fraction effect of the damping affects the dispersion of fluids and enhances the time decay rate of solution. Our method of proof consists of Hodge decomposition technique, L{sup p} − L{sup 2} estimates for the linearized equations, and delicate energy estimates.},

doi = {10.1063/1.4961319},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 57,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4961319

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