Publication: On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications
On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications
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Gérard, P., Kappeler, T., & Topalov, P. (2022). On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications. Nonlinear Analysis: Theory, Methods & Applications, 216, 112687. https://doi.org/10.1016/j.na.2021.112687
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In this paper we prove that the Benjamin-Ono equation admits an analytic Birkhoff normal form in an open neighborhood of zero in H-0(s) (T, R) for any s > -1/2 where H-0(s) (T, R) denotes the subspace of the Sobolev space H-s(T, R) of elements with mean 0. As an application we show that for any -1/2 < s < 0, the flow map of the Benjamin-Ono equation S-0(t) : H-0(s)(T, R) -> H-0(s) (T, R) is nowhere locally uniformly continuous in a neighborhood of zero in H-0(s)(T, R).
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- Gérard, Patrick
- Kappeler, Thomas
- Topalov, Petar
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Gérard, P., Kappeler, T., & Topalov, P. (2022). On the analytic Birkhoff normal form of the Benjamin–Ono equation and applications. Nonlinear Analysis: Theory, Methods & Applications, 216, 112687. https://doi.org/10.1016/j.na.2021.112687
