The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids

Zhen Cheng; Wenjun Wang

doi:10.3934/cpaa.2021151

Article Contents

2021, Volume 20, Issue 12: 4155-4176. Doi: 10.3934/cpaa.2021151

This issue Previous Article Classification of positive radial solutions to a weighted biharmonic equation Next Article Nondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $

The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids

Zhen Cheng and
Wenjun Wang^,

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

^* Corresponding author
^* Corresponding author

Received: March 2021

Revised: August 2021

Early access: September 2021

Published: December 2021

The second author is supported by the National Natural Science Foundation of China (Grant Nos. 11871341 and 12071152)

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Abstract

In this paper, we consider the global existence of the Cauchy problem for a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids in $ \mathbb{R}^3 $. We get the existence theory of global strong solutions by using the decaying properties of the solutions. The energy method combined with the low-high-frequency decomposition is used to derive such properties and hence the global existence. As a byproduct, the optimal time decay estimates of all-order spatial derivatives of the pressure and the velocity are obtained.

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Mathematics Subject Classification: Primary: 76T10, 76N10; Secondary: 35M11.

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