The Cauchy problem for the Kawahara equation with data in analytic Gevrey spaces on the circle is considered and its local well-posedness in these spaces is proved. Using Bourgain-Gevrey type analytic spaces and appropriate bilinear estimates, it is shown that local in time wellposedness holds when the initial data belong to an analytic Gevrey spaces of order σ. Moreover, the solution is not necessarily Gσ in time. However, it belongs to G5σ near zero for every x on the circle. We study a Cauchy problem for Kawahara equation . With data in analytic Gevrey spaces on the circal, we prove that the problem is well defined. We also treat the regularity in time which belongs to $G^{5\sigma}$ .
Kawahara equation Well-posedness Analytic Gevrey spaces Bourgain spaces Bilinear estimates Time regularity
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Publication Date | October 30, 2021 |
Acceptance Date | October 21, 2021 |
Published in Issue | Year 2021 Issue: 2 |
The published articles in MJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ISSN 2667-7660