Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 1

Global strong solution to the Cauchy problem of 1D viscous two-fluid model without any domination condition

Pages: 51 – 70

DOI:  https://dx.doi.org/10.4310/DPDE.2022.v19.n1.a3

Authors

Xiaona Gao (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan Province, China)

Zhenhua Guo (Center for Nonlinear Studies and Department of Mathematics, Northwest University, Xi’an, China)

Zilai Li (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan Province, China)

Abstract

In this paper, we consider the Cauchy problem to the compressible two-fluid Navier–Stokes equations in one-dimensional space allowing vacuum. It is shown that the compressible two-fluid Navier–Stokes equations admit global strong solution with the large initial value and no the domination condition1 which was posed in [A. Vasseur, H.Y. Wen, C. Yu, J. Math. Pure. Appl. 125 (2019), 247–282], when the initial vacuum can be permitted inside the region. Note that this result is proved without any smallness conditions on the initial value.

Keywords

two-fluid model, Cauchy problem, global strong solutions

2010 Mathematics Subject Classification

Primary 76T10. Secondary 35Q30, 76N10.

Z. Guo is supported by the National Natural Science Foundation of China (No. 11931013, 11671319).

Z. Li is supported by the National Natural Science Foundation of China (No.11601128, No.11671319) Fund of Henan Polytechnic University ( No.B2016-57, No.2016XQG-12).

Received 25 August 2021

Published 2 December 2021