We consider the Cauchy problem for the Kirchhoff equation on Td with initial data of small amplitude ϵ in Sobolev class. We prove a lower bound ϵ-4 for the existence time, which improves the bound ϵ-2 given by the standard local theory. The proof relies on a normal form transformation, preceded by a nonlinear transformation that diagonalizes the operator at the highest order, which is needed because of the quasilinear nature of the equation.
Baldi, P., & Haus, E. (2020). On the existence time for the Kirchhoff equation with periodic boundary conditions. NONLINEARITY, 33(1), 196-223 [10.1088/1361-6544/ab4c7b].
Titolo: | On the existence time for the Kirchhoff equation with periodic boundary conditions | |
Autori: | Haus, Emanuele (Corresponding) | |
Data di pubblicazione: | 2020 | |
Rivista: | ||
Citazione: | Baldi, P., & Haus, E. (2020). On the existence time for the Kirchhoff equation with periodic boundary conditions. NONLINEARITY, 33(1), 196-223 [10.1088/1361-6544/ab4c7b]. | |
Handle: | http://hdl.handle.net/11590/365966 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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