论文标题
SQG方程的不变措施和全球良好姿势
Invariant measures and global well posedness for SQG equation
论文作者
论文摘要
我们为表面准藻型（SQG）方程式构建了一个不变的度量$μ$，并表明几乎所有支持$μ$的功能都是SQG全球独特解决方案的初始条件，这些条件是连续取决于初始数据的。此外，我们表明$μ$的支撑是无限的维度，这意味着它不是有限的Hausdorff尺寸的任何紧凑型设置的子集。同样，还有一些全球解决方案具有任意较大的初始条件。 $μ$是通过波动 - 隔离法获得的，即用精心选择的耗散和随机强迫的随机SQG的不变度限制。
We construct an invariant measure $μ$ for the Surface Quasi-Geostrophic (SQG) equation and show that almost all functions in the support of $μ$ are initial conditions of global, unique solutions of SQG, that depend continuously on the initial data. In addition, we show that the support of $μ$ is infinite dimensional, meaning that it is not locally a subset of any compact set with finite Hausdorff dimension. Also, there are global solutions that have arbitrarily large initial condition. The measures $μ$ is obtained via fluctuation-dissipation method, that is, as a limit of invariant measures for stochastic SQG with a carefully chosen dissipation and random forcing.
