论文标题
存在于Hölder和统一局部Sobolev空间中流体方程的解决方案
Existence of Solutions to Fluid Equations in Hölder and Uniformly Local Sobolev Spaces
论文作者
论文摘要
We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the Hölder spaces $C^r(\mathbb{R}^2)$ for $r>1$ and the uniformly local Sobolev spaces $H^s_{ul}(\mathbb{R}^2)$ for $s\geq 3$.使用类似于表面准地藻方程的方法，我们还可以在均匀的局部Sobolev空间中获得三维Euler方程的短期存在。
We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the Hölder spaces $C^r(\mathbb{R}^2)$ for $r>1$ and the uniformly local Sobolev spaces $H^s_{ul}(\mathbb{R}^2)$ for $s\geq 3$. Using methods similar to those for the surface quasi-geostrophic equation, we also obtain short-time existence for the three-dimensional Euler equations in uniformly local Sobolev spaces.
