doi: 10.3934/cpaa.2021072

Remarks on global weak solutions to a two-fluid type model

1. 

School of Mathematics, South China University of Technology, Guangzhou 510641, China

* Corresponding author

Dedicated to Professor Shuxing Chen on the occasion of his 80th birthday

Received  January 2021 Revised  March 2021 Published  April 2021

Fund Project: H. Wen was partially supported by the National Natural Science Foundation of China # 12071152 and #11671150. C. Zhu was partially supported by the National Natural Science Foundation of China #11771150, #11831003 and #11926346, and by Guangdong Basic and Applied Basic Research Foundation #2020B1515310015

The present paper aims to give a review of a two-fluid type model mostly on large-data solutions. Some derivations of the model arising in different physical background will be introduced. In addition, we will sketch the proof of global existence of weak solutions to the Dirichlet problem for the model in one dimension with more general pressure law which can be non-monotone, in the context of allowing unconstrained transition to single-phase flow.

Citation: Huanyao Wen, Changjiang Zhu. Remarks on global weak solutions to a two-fluid type model. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021072
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