Convergence of capillary fluid models: from the non-local to the local Korteweg model
Convergence of capillary fluid models: from the non-local to the local Korteweg model
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毛细管流体模型的收敛：从非局部到局部 Korteweg 模型
DOI：
10.1512/iumj.2011.60.4600
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
B. Haspot
中科院分区：
文献类型：
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作者：
Frédéric Charve;B. Haspot
本文研究了具有非局部毛细张量的正压可压缩Navier-Stokes系统，该系统依赖于一个小参数$\epsilon$，使得它启动性地趋向于局部Korteweg系统。在给出与非经典冲击理论相关的一些物理动机（参见[28]）之后，我们证明了非局部模型的全局适定性（在整个空间$R^d$与$d\geq 2$），并且我们还证明了当$\epsilon$趋于零时，局部Korteweg系统解的收敛性。
In this paper we are interested in the barotropic compressible Navier-Stokes system endowed with a non-local capillarity tensor depending on a small parameter $\epsilon$ such that it heuristically tends to the local Korteweg system. After giving some physical motivations related to the theory of non-classical shocks (see [28]) we prove global well-posedness (in the whole space $R^d$ with $d\geq 2$) for the non-local model and we also prove the convergence, as $\epsilon$ goes to zero, to the solution of the local Korteweg system.