文献类型：期刊文献

英文题名：Existence of strong solutions to the stationary compressible Navier-Stokes-Korteweg equations with large external force

作者：Li, Yeping[1];Liao, Jie[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2019

卷号：47

起止页码：204

外文期刊名：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

收录：;EI(收录号：20184706106209);WOS:【SCI-EXPANDED(收录号:WOS:000458714100012)】；

基金：The research of Li is partially supported by the National Science Foundation of China (Grant No. 11671134). The research of Liao is partially supported by Fundamental Research Funds for the Central Universities.

语种：英文

外文关键词：Compressible; Navier-Stokes-Korteweg equation; Existence; Zero mach number limit; Large external force

摘要：In this study, we show the existence of strong solution to the boundary value problem of the steady compressible Navier-Stokes-Korteweg equation with large external forces in bounded domain, provided that the Mach number is appropriately small. Moreover, the Mach number limit of the strong solutions is rigorously verified. The main idea in the proof is to split the original equation into two parts: (i) a system of stationary incompressible Navier-Stokes-Korteweg equations with large forces, (ii) a system of stationary compressible Navier-Stokes-Korteweg equations with small forces. Introducing the "modified pressures", (i) is reduced to a system of stationary incompressible Navier-Stokes equations with large forces coupled with an elliptic equation, (ii) is reduced to a system of stationary compressible Navier-Stokes equations with small forces coupled with an elliptic equation. Based on the known results for linear incompressible Navier-Stokes equation, linear transport equation and elliptic equation, we establish uniformity in the Mach number a priori estimates. Further, using the Schauder fixed point theorem, we present the existence of a strong solution. At the same time, from the uniform a priori estimates, we show the zero Mach number limit of the strong solutions, which converge to the solutions of the corresponding incompressible Navier-Stokes-Korteweg equations. (C) 2018 Published by Elsevier Ltd.