Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow

Long Fan; Cheng-Jie Liu; Lizhi Ruan; Long Fan; Cheng-Jie Liu; Lizhi Ruan

doi:10.3934/era.2021070

Electronic Research Archive

2021, Volume 29, Issue 6: 4009-4050. doi: 10.3934/era.2021070

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Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow

1.
The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
2.
School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
3.
School of Mathematical Sciences, Institute of Natural Sciences, Center of Applied Mathematics
4.
MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China
5.
Hong Kong Institute for Advanced Study, City University of Hong Kong, Hong Kong, China
6.
The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received: 01 May 2021 Published: 07 September 2021
35A01, 35A02, 35G61, 35M13

In this paper, we consider the two-dimensional (2D) two-fluid boundary layer system, which is a hyperbolic-degenerate parabolic-elliptic coupling system derived from the compressible isentropic two-fluid flow equations with nonslip boundary condition for the velocity. The local existence and uniqueness is established in weighted Sobolev spaces under the monotonicity assumption on tangential velocity along normal direction based on a nonlinear energy method by employing a nonlinear cancelation technic introduced in [R. Alexandre, Y.-G. Wang, C.-J. Xu and T. Yang, J. Amer. Math. Soc., 28 (2015), 745-784; N. Masmoudi and T.K. Wong, Comm. Pure Appl. Math., 68(2015), 1683-1741] and developed in [C.-J. Liu, F. Xie and T. Yang, Comm. Pure Appl. Math., 72(2019), 63-121].
- Two-fluid boundary layer system,
- local well-posedness,
- weighted energy method
Citation: Long Fan, Cheng-Jie Liu, Lizhi Ruan. Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow[J]. Electronic Research Archive, 2021, 29(6): 4009-4050. doi: 10.3934/era.2021070

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Abstract

In this paper, we consider the two-dimensional (2D) two-fluid boundary layer system, which is a hyperbolic-degenerate parabolic-elliptic coupling system derived from the compressible isentropic two-fluid flow equations with nonslip boundary condition for the velocity. The local existence and uniqueness is established in weighted Sobolev spaces under the monotonicity assumption on tangential velocity along normal direction based on a nonlinear energy method by employing a nonlinear cancelation technic introduced in [R. Alexandre, Y.-G. Wang, C.-J. Xu and T. Yang, J. Amer. Math. Soc., 28 (2015), 745-784; N. Masmoudi and T.K. Wong, Comm. Pure Appl. Math., 68(2015), 1683-1741] and developed in [C.-J. Liu, F. Xie and T. Yang, Comm. Pure Appl. Math., 72(2019), 63-121].

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