Leray weak solutions of the Incompressible Navier Stokes system on exterior domains via the artificial compressibility method
Leray weak solutions of the Incompressible Navier Stokes system on exterior domains via the artificial compressibility method
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不可压缩纳维斯托克斯系统在外域上通过人工压缩方法的 Leray 弱解
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
P. Marcati
中科院分区：
文献类型：
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作者：
D. Donatelli;P. Marcati
本文研究了不可压Navier-Stokes方程在外部区域上的Leray弱解，特别描述了J. L. Lions和Temam提出的人工压缩方法的双曲形式.由于声波的存在，这些类型的近似的收敛性通常显示出缺乏强收敛性。在本文中，我们面对这一困难，照顾这些波的色散性质的装置的Escherichartz估计或波方程满足的压力。我们实际上将压力分解在不同的声学分量中，每一个声学分量都满足一个特定的初边值问题。利用相应的Leray-Hodge分解，可得到速度场的强收敛性分析。
In this paper we study the Leray weak solutions of the incompressible Navier Stokes equation in an exterior domain.We describe, in particular, an hyperbolic version of the so called artificial compressibility method investigated by J.L.Lions and Temam. The convergence of these type of approximation show in general a lack of strong convergence due to the presence of acoustic waves. In this paper we face this difficulty by taking care of the dispersive nature of these waves by means of the Strichartz estimates or waves equations satisfied by the pressure. We actually decompose the pressure in different acoustic components, each one of them satisfies a specific initial boundary value problem. The strong convergence analysis of the velocity field will be achieved by using the associated Leray-Hodge decomposition.