LOCAL WELL-POSEDNESS OF SOLUTIONS TO THE BOUNDARY LAYER EQUATIONS FOR COMPRESSIBLE TWO-FLUID FLOW

被引：0

作者：

Fan, Long ^{[1
,2
]}

Liu, Cheng-Jie ^{[3
,4
]}

Ruan, Lizhi ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Peoples R China

[2] Shanxi Datong Univ, Sch Math & Stat, Datong 037009, Peoples R China

[3] Shanghai Jiao Tong Univ, Sch Math Sci, Inst Nat Sci, Ctr Appl Math,MOE,LSC, Shanghai 200240, Peoples R China

[4] Shanghai Jiao Tong Univ, SHL, MAC, Shanghai 200240, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 06期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Two-fluid boundary layer system; local well-posedness; weighted energy method; NAVIER-STOKES EQUATION; ZERO VISCOSITY LIMIT; PRANDTL EQUATIONS; ILL-POSEDNESS; GLOBAL EXISTENCE; ANALYTIC SOLUTIONS; HALF-SPACE; STABILITY; EULER;

D O I：

10.3934/era.2021070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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].

引用

页码：4009 / 4050

页数：42

共 50 条

[31] Local Well-posedness for Linearized Degenerate MHD Boundary Layer Equations in Analytic Setting
Ya Jun LI
Wen Dong WANG
ActaMathematicaSinica, 2019, 35 (08) : 1402 - 1418
[32] GLOBAL WELL-POSEDNESS IN CRITICAL BESOV SPACES FOR TWO-FLUID EULER-MAXWELL EQUATIONS
Xu, Jiang
Xiong, Jun
Kawashima, Shuichi
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (03) : 1422 - 1447
[33] Local Well-Posedness of Strong Solutions for the Nonhomogeneous MHD Equations with a Slip Boundary Conditions
Li, Hongmin
Xiao, Yuelong
ACTA MATHEMATICA SCIENTIA, 2020, 40 (02) : 442 - 456
[34] Local Well-Posedness of Strong Solutions for the Nonhomogeneous MHD Equations with a Slip Boundary Conditions
Hongmin Li
Yuelong Xiao
Acta Mathematica Scientia, 2020, 40 : 442 - 456
[35] LOCAL WELL-POSEDNESS OF STRONG SOLUTIONS FOR THE NONHOMOGENEOUS MHD EQUATIONS WITH A SLIP BOUNDARY CONDITIONS
李红民
肖跃龙
Acta Mathematica Scientia, 2020, 40 (02) : 442 - 456
[36] ON THE WELL-POSEDNESS AND DECAY RATES OF STRONG SOLUTIONS TO A MULTI-DIMENSIONAL NON-CONSERVATIVE VISCOUS COMPRESSIBLE TWO-FLUID SYSTEM
Xu, Fuyi
Chi, Meiling
Liu, Lishan
Wu, Yonghong
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (05) : 2515 - 2559
[37] Local well-posedness of the vacuum free boundary of 3-D compressible Navier–Stokes equations
Guilong Gui
Chao Wang
Yuxi Wang
Calculus of Variations and Partial Differential Equations, 2019, 58
[38] The well-posedness of incompressible one-dimensional two-fluid model
Song, JH
Ishii, M
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2000, 43 (12) : 2221 - 2231
[39] Local Well-Posedness for the Compressible Nematic Liquid Crystals Flow with Vacuum
Jishan Fan
Fucai Li
Gen Nakamura
Analysis in Theory and Applications, 2020, 36 (04) : 497 - 509
[40] Local Well-Posedness for the Compressible Nematic Liquid Crystals Flow with Vacuum
Fan, Jishan
Li, Fucai
Nakamura, Gen
ANALYSIS IN THEORY AND APPLICATIONS, 2020, 36 (04) : 497 - 509

← 1 2 3 4 5 →