Large deviations principle for the invariant measures of the 2D stochastic Navier–Stokes equations with vanishing noise correlation
Large deviations principle for the invariant measures of the 2D stochastic Navier–Stokes equations with vanishing noise correlation
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DOI：
10.1007/s40072-021-00219-5
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
S. Cerrai;N. Paskal
中科院分区：
文献类型：
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作者：
S. Cerrai;N. Paskal
本文研究了圆环面上二维不可压Navier-Stokes方程，该方程受时间上为白色、空间上为有色的高斯噪声驱动。我们考虑了随机强迫的大小及其相关尺度都很小的情况。我们证明了一个大偏差原则的解决方案，以及家庭不变的措施，asandare同时发送到0，在适当的缩放。
We study the two-dimensional incompressible Navier–Stokes equation on the torus, driven by Gaussian noise that is white in time and colored in space. We consider the case where the magnitude of the random forcingand its correlation scaleare both small. We prove a large deviations principle for the solutions, as well as for the family of invariant measures, asandare simultaneously sent to 0, under a suitable scaling.