论文标题
估计超临界表面quasigeSostrophic方程的奇异集的尺寸
Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation
论文作者
论文摘要
我们考虑由$α<\ frac {1} {2} $的分数拉普拉斯给出的SQG方程。我们引入了一个合适的弱解决方案的概念，该概念在每$ l^2 $初始基准中都存在，并且我们证明，对于这种解决方案，单数集包含在Hausdorff Dimension的时空集合中，最多可达$ \ frac {1} {1} {2α} {2α} \ left（\ frac {\ frac {\ frac {1 +α}α（1 +α}α（1-2-2α）$ 2 \ \ 2 \ y 2 \）
We consider the SQG equation with dissipation given by a fractional Laplacian of order $α<\frac{1}{2}$. We introduce a notion of suitable weak solution, which exists for every $L^2$ initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most $\frac{1}{2α} \left( \frac{1+α}α (1-2α) + 2\right)$.
