Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System

作     者：Song JIANG Xiangxiang SU Feng XIE Song JIANG;Xiangxiang SU;Feng XIE

作者机构：Institute of Applied Physics and Computational MathematicsBeijing 100088China School of Mathematical SciencesShanghai Jiao Tong UniversityShanghai 200240China School of Mathematical SciencesCMA-ShanghaiShanghai Jiao Tong UniversityShanghai 200240China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2023年第44卷第5期

页      面：663-686页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0701[理学-数学] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.12271359,11831003,12161141004,11631008) Shanghai Science and Technology Innovation Action Plan(No.20JC1413000) the National Key R&D Program(No.2020YFA0712200) the National Key Project(No.GJXM92579) the Sino-German Science Center(No.GZ 1465) the ISF-NSFC Joint Research Program(No.11761141008) 

主　　题：Sharp interface limit Incompressible Navier-Stokes equations AllenCahn equation Spectral estimate Energy estimates 

摘      要：The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this *** the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev *** the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error *** convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.