Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

作     者：Ya-zhou Chen Hakho Hong Xiao-ding Shi Ya-zhou CHEN;Hakho HONG;Xiao-ding SHI

作者机构：Department of MathematicsCollege of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China Institute of MathematicsState Academy of SciencesPyongyangKorea 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2024年第40卷第1期

页      面：45-74页

核心收录：

学科分类：080704[工学-流体机械及工程] 08[工学] 0807[工学-动力工程及工程热物理] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (Nos. 12171024, 11901025,11971217, 11971020) Academic and Technical Leaders Training Plan of Jiangxi Province (No. 20212BCJ23027) 

主　　题：Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate 

摘      要：This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.