The second grade fluid and averaged Euler equations with Navier-slip boundary conditions
The second grade fluid and averaged Euler equations with Navier-slip boundary conditions
复制标题
DOI：
10.1088/0951-7715/16/3/318
复制
发表时间：
2003-05
期刊：
影响因子：
1.7
通讯作者：
A. Busuioc;T. Ratiu
中科院分区：
文献类型：
--
作者：
A. Busuioc;T. Ratiu
我们研究了有黏度和无黏度的Navier-slip边界条件下二级流体在d， d = 2,3有界域中的运动方程（平均欧拉方程）。我们证明了二维H3解的整体存在唯一性。在三维空间中，我们得到了任意初始数据下H3解的局部存在性，以及小初始数据和正粘度下H3解的全局存在性。最后，我们找到了平均欧拉方程平稳解的Liapunov稳定性条件，类似于经典欧拉方程的Rayleigh-Arnold稳定性结果。
We study the equations governing the motion of second grade fluids in a bounded domain of d, d = 2,3, with Navier-slip boundary conditions with and without viscosity (averaged Euler equations). We show global existence and uniqueness of H3 solutions in dimension two. In dimension three, we obtain local existence of H3 solutions for arbitrary initial data and global existence for small initial data and positive viscosity. We close by finding Liapunov stability conditions for stationary solutions for the averaged Euler equations similar to the Rayleigh–Arnold stability result for the classical Euler equations.