2. Improved Lower Bounds for the Uniform Radius of Spatial Analyticity of the Modified Camassa-Holm Equation
Author: Tegegne Getachew DOWNLOAD
DOI:
Abstract
We show that the uniform radius of spatial analyticity, σ(t), of the solutions at time t for the modified Camassa-Holm equation is bounded below
by c|t|− 1 2γ for large t, where γ is a value in the interval (−0,1], provided the initial data is analytic with a fixed radius σ0. To establish this lower bound, we
use the standard contraction mapping principle, an approximate conservation law in the modified Gevrey space Hσ,1, linear estimates, a Strichartz estimate,
the Transference principle, and Sobolev embedding. This result enhances the findings of Himonas and Petronilho, as well as Getachew.
Keywords
Modified CH equation; Modified Gevrey spaces; Strichartz estimate; Transference principle; Uniform radius of spatial analyticity.