The incompressible limit in $$L^p$$Lp type critical spaces
The incompressible limit in $$L^p$$Lp type critical spaces
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DOI：
10.1007/s00208-016-1361-x
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发表时间：
2014-09
影响因子：
1.4
通讯作者：
R. Danchin;Lingbing He
中科院分区：
文献类型：
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作者：
R. Danchin;Lingbing He
本文旨在证明不可压粘性可压缩流动的Navier-Stokes方程在他们准备不充分的边界层中的低马赫数收敛性。流体域可以是整个空间，也可以是环面。一些作品一直致力于这一经典问题，所有这些都是，据我们所知，有关tospaces和能源类型的论点。本文在临界正则性框架下研究了低马赫数收敛问题。更确切地说，在正压情况下，初始速度场的无发散部分只需在临界Besov空间中有界，但由于声波的存在，我们仍然需要速度势部分的低频和密度的类型界，这一假设在准备不足的数据框架中似乎是不可避免的。在本文的最后一部分，我们的结果被推广到热传导流体的完整的Navier-Stokes系统。
This paper aims at justifying the low Mach number convergence to the incompressible Navier–Stokes equations for viscous compressible flows in theill-prepared datacase. The fluid domain is either the whole space, or the torus. A number of works have been dedicated to this classical issue, all of them being, to our knowledge, related tospaces and to energy type arguments. In the present paper, we investigate the low Mach number convergencein thetype critical regularity framework. More precisely, in the barotropic case, the divergence-free part of the initial velocity field just has to be bounded in the critical Besov spacefor some suitableWe still requiretype bounds on the low frequencies of the potential part of the velocity and on the density, though, an assumption which seems to be unavoidable in the ill-prepared data framework, because of acoustic waves. In the last part of the paper, our results are extended to the full Navier–Stokes system for heat conducting fluids.