Hao Jia
We reformulate results from the paper ``Linear vortex symmetrization: The spectral density function" by Ionescu and the author in simplified forms and derive rigorously the bounds given in Bassom and Gilbert (J. Fluid Mech., 1998), which provided interesting insights on the vortex symmetrization phenomenon.
This paper contains 3 sections, 3 theorems, 66 equations.
Theorem 1.2
Assume that $k\in\mathbb{Z}\cap[1,\infty)$, and that $\omega_{0k}(r)$ is smooth for $r\in(0,\infty)$ and satisfies the Gevrey regularity bounds in $v=\log r\in\mathbb{R}$, in MPro3 and MARr2-MARr3 below. Let $\omega_k(t,r)\in C^\infty([0,\infty)\times (0,\infty))$ be the unique solution to B4 with i In the above, $M_k$ is the weighted Gevrey-2 norm of $\omega_{0k}$ in the variable $v=\log r$, give
