Long time bounds for the periodic Benjamin–Ono–BBM equation

Mammeri, Youcef

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.na.2009.03.078

Title :

Long time bounds for the periodic Benjamin–Ono–BBM equation

Author(s) :

Mammeri, Youcef [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Nonlinear Analysis: Theory, Methods and Applications

Pages :

5010 - 5021

Publisher :

Elsevier

Publication date :

2009

ISSN :

0362-546X

English keyword(s) :

BO-BBM equation
KP equations
local and global well-posedness
long time bounds

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We consider the periodic Benjamin-Ono equation, regularized in the same manner the Benjamin-Bona-Mahony equation is found from the Korteweg-de Vries one, namely the equation $u_t + u_x + \alpha u u_x + \beta H(u_{xt})=0,$ ...
Show more >We consider the periodic Benjamin-Ono equation, regularized in the same manner the Benjamin-Bona-Mahony equation is found from the Korteweg-de Vries one, namely the equation $u_t + u_x + \alpha u u_x + \beta H(u_{xt})=0,$ where $H$ is the Hilbert transform, $\alpha$ the quotient between the characteristic waves amplitude and the depth of the waves and $\beta$ the quotient between this depth and the wavelength. We show that the solution, starting from an initial datum of size $\varepsilon$, remains smaller than $\varepsilon$ for a time scale of order $\left(\varepsilon^{-1}\frac{\beta}{\alpha}\right)^2$, whereas the local well-posedness gives only a time of order $\varepsilon ^{-1}\frac{\beta}{\alpha}$.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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