Paracontrolled quasi-geostrophic equation with space-time white noise
Paracontrolled quasi-geostrophic equation with space-time white noise
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DOI：
10.4064/dm806-7-2020
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发表时间：
2018-06
影响因子：
1.8
通讯作者：
Y. Inahama;Y. Sawano
中科院分区：
文献类型：
--
作者：
Y. Inahama;Y. Sawano
研究了二维环面上具有时空白噪声的随机耗散拟地转方程。这个方程是高度奇异的，在其原始形式中基本上是病态的。本文的主要目的是在副控制微积分的框架下，在主项分数阶拉普拉斯函数的微分阶大于$7/4$时，在时间上局部地表述和求解这个方程。这个模型不需要进行重整化。
We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus. This equation is highly singular and basically ill-posed in its original form. The main objective of the present paper is to formulate and solve this equation locally in time in the framework of paracontrolled calculus when the differential order of the main term, the fractional Laplacian, is larger than $7/4$. No renormalization has to be done for this model.