论文标题
改进的Hausdorff维度估计值的超临界表面quasigeostrophic方程
Improved Hausdorff dimension estimate of the singular set of the supercritical surface quasigeostrophic equation
论文作者
论文摘要
我们证明，任何合适的leray-hopf解决方案的时空奇异集，并通过分数耗散$ 0 <α<\ frac {1} {2} $具有hausdorff dimension $ 0 <α<\ frac {1} {1} {2} $最多$ \ frac {1} {1} {2α^2} \ $ nip的构建。衰减结果和对粒子流量的控制已经发展。改进在于当地能源不平等的初始迭代，类似于Navier-Stokes方程的Caffarelli-Kohn-Nirenberg [2]的著名结果。
We prove that the spacetime singular set of any suitable Leray-Hopf solution of the surface quasigeostrophic equation with fractional dissipation of order $0< α< \frac{1}{2}$ has Hausdorff dimension at most $\frac{1}{2α^2}\,.$ This result improves previously known dimension estimate established in [6] and builds on the excess decay result and the control on the particle flow already developed there. The improvement lies in the initial iteration of the local energy inequality in analogy with the celebrated result of Caffarelli-Kohn-Nirenberg [2] for the Navier-Stokes equations.
