Incompressible limit on thin domains with periodic boundary condition
Incompressible limit on thin domains with periodic boundary condition
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DOI：
10.1088/1361-6544/ac14a0
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发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Sai Li;Yang Li
中科院分区：
文献类型：
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作者：
Sai Li;Yang Li
本文研究了具有一般初值的周期性薄区域Ωδ= Ta ~ 2 ×δT上不可压缩粘性流动的Navier-Stokes方程/Euler方程的收敛性。与Caggio等人（2020 Nonlinearity 33 840-863）在整个空间中考虑类似问题相比，我们必须处理声波的持久性。我们证明了当马赫数ε为0以及厚度δ/粘性为0时，三维区域中的弱解弱/强收敛于二维不可压Navier-Stokes方程/Euler方程的解.
We consider convergence to the incompressible Navier–Stokes equations/Euler equations for compressible viscous flows on periodic thin domain Ωδ=Ta2×δT with general initial data. Compared with Caggio et al (2020 Nonlinearity 33 840–863), where similar problems are considered in the whole space, we have to deal with the persistence of acoustic waves. We prove that the weak solutions in the 3D domain converge weakly/strongly to the solutions of the 2D incompressible Navier–Stokes equations/Euler equations when the Mach number ɛ goes to 0 as well as the thickness δ/the viscosity goes to 0.