Continuation of Time Bounds for a Regularized Boussinesq System - Archive ouverte HAL Access content directly
Journal Articles Acta Applicandae Mathematicae Year : 2012

Continuation of Time Bounds for a Regularized Boussinesq System

Abstract

We study the periodic solution of a perturbed regularized Boussinesq system, namely the system $ \eta_t + u_x + \beta (-\eta_{xxt} + u_{xxx}) + \alpha ( (\eta u)_x + \eta \eta_x + u u_x ) = 0, u_t + \eta_x + \beta (\eta_{xxx} - u_{xxt}) + \alpha ( (\eta u)_x + \eta \eta_x + u u_x) =0,$ with $0<\alpha, \beta \leq 1$. We prove that the solution, starting from an initial datum of size $\varepsilon$, remains smaller than $\varepsilon$ for a time scale of order $(\ varepsilon^{-1} \alpha^{-1} \beta )^2$, whereas the natural time is of order $\ varepsilon ^{-1}\alpha^{-1}\beta$.
Fichier principal
Vignette du fichier
2011_10_NormBouss_preprint.pdf (293.36 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01090364 , version 1 (03-12-2014)

Identifiers

Cite

Youcef Mammeri. Continuation of Time Bounds for a Regularized Boussinesq System. Acta Applicandae Mathematicae, 2012, 117, pp.1 - 13. ⟨10.1007/s10440-011-9647-1⟩. ⟨hal-01090364⟩
29 View
72 Download

Altmetric

Share

Gmail Facebook X LinkedIn More