论文标题
傅里叶空间中关键耗散质量地球方程的渐近行为
Asymptotic behavior of critical dissipative quasi-geostrophic equation in Fourier space
论文作者
论文摘要
在本文中，如果$ \ | \ | \ wideHat {θ^0} \ | _ {l^1} $，我们显示了关键耗散准化地方程的全局存在；除其他外，我们证明了这种解决方案的分析性。如果此外，初始条件还验证了$ | d |^{ - δ}θ^0 \ in L^1（\ Mathbb r^2）$带有$ 0 <δ<1 $，则该解决方案保持规律，$ \ lim_ {t \ rightArrow \ rightarrow \ rightarrow \ infty} t^t^Δ使用傅立叶分析和标准技术。
In this paper we show the global existence for critical dissipative quasi-geostrophic equations if $\|\widehat{θ^0}\|_{L^1}$ is small enough; among others we prove the analyticity of such a solution. If in addition the initial condition verifies $|D|^{-δ}θ^0\in L^1(\mathbb R^2)$ with $0<δ<1$, then the solution remains regular and $\lim_{t\rightarrow\infty}t^δ\|\widehatθ(t)\|_{L^1}=0$. Fourier analysis and standard techniques are used.
