Lower bounds on the radius of spatial analyticity for the modified Kawahara equation
• Yantao Guo,
• Huichao Wang
Yantao Guo
Xuchang University

Corresponding Author:gythust@163.com

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Huichao Wang
Xuchang University
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## 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|→∞.