Lower bounds on the radius of spatial analyticity for the modified
Kawahara equation
Abstract
We consider the cauchy problem for the modified Kawahara equation with
cubic nonlinear term in analytic Gevrey space. Utilizing linear and
trilinear estimates in analytic Bourgain-Gevrey space, we establish the
local well-posedness in Gevrey space G δ , s and show the radius of
spatial analyticity persists during the lifespan. Finally, using an
approximate conservation law, we extend this to a global result in such
a way that the radius of analyticity of solutions is uniformly bounded,
that the uniform radius of spatial analyticity of solutions at later
time t can decay no faster than 1 /|
t| as | t|→∞.