Evolution of the radius of spatial analyticity for the periodic BBM equation

Himonas, A.; Petronilho, Gerson

doi:10.1090/proc/14942

Evolution of the radius of spatial analyticity for the periodic BBM equation
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by A. Alexandrou Himonas and Gerson Petronilho

Proc. Amer. Math. Soc. 148 (2020), 2953-2967

DOI: https://doi.org/10.1090/proc/14942

Published electronically: February 26, 2020

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Abstract:

The Cauchy problem of the Benjamin-Bona-Mahony (BBM) equation with initial data $u_0$ that are analytic on the torus and have uniform radius of analyticity $r_0$ is considered, and the evolution of the radius of spatial analyticity $r(t)$ of the solution $u(t)$ at any future time $t$ is examined. It is shown that the size of the radius of spatial analyticity persists for some time and after that it evolves in a such a way that its size at any time $t$ is bounded below by $c t^{-1}$ for some $c>0$. The optimality of this bound remains an open question.

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