American Institute of Mathematical Sciences

December  2021, 29(6): 4009-4050. doi: 10.3934/era.2021070

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

* Corresponding author: Lizhi Ruan, rlz@mail.ccnu.edu.cn

Received  May 2021 Published  December 2021 Early access  September 2021

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].

Citation: Long Fan, Cheng-Jie Liu, Lizhi Ruan. Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow. Electronic Research Archive, 2021, 29 (6) : 4009-4050. doi: 10.3934/era.2021070
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