Abstract
We study the periodic solution of a perturbed regularized Boussinesq system (Bona et al., J. Nonlinear Sci. 12:283–318, 2002, Bona et al., Nonlinearity 17:925–952, 2004), namely the system η t +u x +β(−η xxt +u xxx )+α((ηu) x +ηη x +uu x )=0,u t +η x +β(η xxx −u xxt )+α((ηu) x +ηη x +uu x )=0, with 0<α,β≤1. We prove that the solution, starting from an initial datum of size ε, remains smaller than ε for a time scale of order (ε −1 α −1 β)2, whereas the natural time is of order ε −1 α −1 β.
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Mammeri, Y. Continuation of Time Bounds for a Regularized Boussinesq System. Acta Appl Math 117, 1–13 (2012). https://doi.org/10.1007/s10440-011-9647-1
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DOI: https://doi.org/10.1007/s10440-011-9647-1