论文标题
随机二年级流体方程的无知极限
Inviscid Limit for Stochastic Second-Grade Fluid Equations
论文作者
论文摘要
我们在平滑且有界的二维结构域中考虑$ l^2 $ norm中的收敛时间（随时间均匀地，随机的二年级流体方程，带有传输噪声和无滑界边界条件的解决方案。我们证明，假设欧拉方程的初始条件的适当规律性以及参数$ν$和$α$的适当行为，则无关限制的限制在不需要特定耗散边界层中二级流体方程的溶液的能量的情况下。
We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove, that assuming proper regularity of the initial conditions of the Euler equations and a proper behavior of the parameters $ν$ and $α$, then the inviscid limit holds without requiring a particular dissipation of the energy of the solutions of the second-grade fluid equations in the boundary layer.
