Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law
Existence of smooth solutions for the compressible barotropic Navier-Stokes-Korteweg system without increasing pressure law
复制标题
不增加压力定律的可压缩正压 Navier-Stokes-Korteweg 系统光滑解的存在性
DOI：
10.1002/mma.6252
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发表时间：
2020
影响因子：
2.9
通讯作者：
Shi Xiaoding（施小丁）
中科院分区：
文献类型：
--
作者：
Huang Feimin;Hong Hakho;Shi Xiaoding（施小丁）
本文考虑毛细可压缩流体的正压模型，在一般压力定律下，考虑货车德瓦尔斯气体，描述具有扩散界面的液-汽混合物的动力学。在尽可能接近物理能量空间的Sobolev空间中，利用线性化系统的估计和压缩映射原理，首先证明了中Cauchy问题的光滑解的局部存在唯一性.其次，利用局部解的延拓论证，证明了环面上周期条件的初边值问题存在整体唯一解。注意，压力不是密度ρ的增函数是主要的困难之一。
This paper is concerned with a barotropic model of capillary compressible fluids describing the dynamics of a liquid‐vapor mixture with diffuse interphase, in the case of general pressure law including Van der Waals gas. In the Sobolev spaces as close as possible to the physical energy spaces, we first prove local in time existence and uniqueness of the smooth solutions to the Cauchy problem in, based on the estimates of a linearized system and the contraction mapping principle. Next, we show that there exists a global unique solution for the initial boundary value problem with periodic conditions in torus, by using a continuation argument of local solution. Notice that it is one of the main difficulties that pressurepis not increasing function of densityρ.