论文标题
在$ \ mathbb {r}^2 $中的不可压缩粘性流体和图形上的Spdes，在有快速的平流和非平滑噪声的情况下
Incompressible viscous fluids in $\mathbb{R}^2$ and SPDEs on graphs, in presence of fast advection and non smooth noise
论文作者
论文摘要
研究了平面中一类随机反应扩散 - 辅助方程的渐近行为。我们表明，随着无差的对流术语变得越来越大，此类方程的解决方案会收敛到与Hamiltonian相关的图上定义的合适随机PDE的溶液。首先，我们处理这样的情况：随机扰动是通过在Schwartz分布空间中的奇异空间均匀的维纳过程给出的。与以前的作品一样，我们在这里假设运动时期的衍生物在哈密顿式的水平集上并不消失。然后，在第二部分中，在不假定该时期的导数的情况下，我们研究了合适的线性SPDES溶液的收敛类型较弱。
The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the solution of a suitable stochastic PDE defined on the graph associated with the Hamiltonian. Firstly, we deal with the case that the stochastic perturbation is given by a singular spatially homogeneous Wiener process taking values in the space of Schwartz distributions. As in previous works, we assume here that the derivative of the period of the motion on the level sets of the Hamiltonian does not vanish. Then, in the second part, without assuming this condition on the derivative of the period, we study a weaker type of convergence for the solutions of a suitable class of linear SPDEs.
