Open AccessLocal well-posedness of solutions to the boundary layer equations for compressible two-fluid flow
Author(s) -
Long Fan,
Chengjie Liu,
Lizhi Ruan
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021070
Subject(s) - uniqueness , sobolev space , mathematics , degenerate energy levels , compressibility , boundary (topology) , nonlinear system , mathematical analysis , boundary layer , compressible flow , flow (mathematics) , monotonic function , energy (signal processing) , geometry , physics , mechanics , quantum mechanics , statistics
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].