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

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- by A. Alexandrou Himonas and Gerson Petronilho PDF
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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.## References

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## Additional Information

**A. Alexandrou Himonas**- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 86060
- Email: himonas.1@nd.edu
**Gerson Petronilho**- Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil
- MR Author ID: 250320
- Email: gerson@dm.ufscar.br
- Received by editor(s): January 14, 2019
- Received by editor(s) in revised form: November 16, 2019
- Published electronically: February 26, 2020
- Additional Notes: The first author was partially supported by a grant from the Simons Foundation (#524469)

The second author was partially supported by grant 303111/2015-1, CNPq, and grant 2012/03168-7, São Paulo Research Foundation (FAPESP) - Communicated by: Catherine Sulem
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 2953-2967 - MSC (2010): Primary 35Q53, 37K10
- DOI: https://doi.org/10.1090/proc/14942
- MathSciNet review: 4099783