On singular limit equations for incompressible fluids in moving thin domains
On singular limit equations for incompressible fluids in moving thin domains
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运动薄域中不可压缩流体的奇异极限方程
DOI：
10.1090/qam/1495
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发表时间：
2018
影响因子：
0.8
通讯作者：
T.-H. Miura
中科院分区：
文献类型：
--
作者：
T.-H. Miura;Y. Giga;and C. Liu;T.-H. Miura
本文考虑三维运动薄区域中的不可压Euler方程和Navier-Stokes方程。在假设薄区域的宽度趋于零时，薄区域退化为二维移动闭曲面的条件下，给出了薄区域中Euler方程和Navier-Stokes方程退化移动曲面上的奇异极限方程的启发式推导，并研究了它们的能量结构之间的关系.我们还比较了稳定流形上的欧拉和Navier-Stokes方程的极限方程，这是描述的Levi-Civita连接。
We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin domain goes to zero, we give a heuristic derivation of singular limit equations on the degenerate moving surface of the Euler and Navier-Stokes equations in the moving thin domain and investigate relations between their energy structures. We also compare the limit equations with the Euler and Navier-Stokes equations on a stationary manifold, which are described in terms of the Levi-Civita connection.