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Asymptotic behavior of small solutions of the Benjamin–Ono equation with time-dependent coefficients

Mammeri Y.

Journal of Applied Analysis

2015

Vol. 21, nr 1

9--23

We study the behavior of small solutions depending on time of the generalized and regularized Benjamin–Ono equation in both continuous and periodic context. In particular, we prove that these solutions remain small for a time scale improving the natural time given by the localwell-posedness. In the continuous case, the result becomes global-in-time.