Global solutions of a surface quasigeostrophic front equation
Global solutions of a surface quasigeostrophic front equation
复制标题
DOI：
10.2140/paa.2021.3.403
复制
发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
J. K. Hunter;Jingyang Shu;Qingtian Zhang
中科院分区：
文献类型：
--
作者：
J. K. Hunter;Jingyang Shu;Qingtian Zhang
考虑$\mathbb{R}$上一维空间的非线性、空间非局部初值问题，该问题描述了地表准地转锋（SQG）的运动。在方程非线性项的多元线性展开的收敛条件下，证明了初值问题具有唯一的局部光滑解，并且在足够光滑且初始数据较小的情况下，证明了这些解是全局的。
We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has unique local smooth solutions under a convergence condition on the multilinear expansion of the nonlinear term in the equation, and, for sufficiently smooth and small initial data, we prove that these solutions are global.