On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids

被引：17
作者：
Antonelli, Paolo [1 ]
Spirito, Stefano [2 ]
机构：
[1] GSSI, Viale Francesco Crispi 7, I-67100 Laquila, Italy
[2] DISIM, Via Vetoio, I-67100 Laquila, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 187卷
关键词：
Compressible fluids; Navier-Stokes-Korteweg; Capillarity; Vacuum; Compactness; SYSTEM; POSEDNESS; EXISTENCE; MODEL;
D O I：
10.1016/j.na.2019.03.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. In contrast with previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The compactness is obtained by introducing suitable truncations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：110 / 124
页数：15
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