KdV and BO equations with bore-like data. (English) Zbl 1022.35059

Iorio, R.; Linares, F.; Scialom, M.

Differ. Integral Equ. 11, No. 6, 895-915 (1998).

The authors prove the global well-posedness of the initial value problem for the Korteweg-de Vries (KdV) equation with initial conditions of a special type. These are functions \(g\) satisfying { (i)} \( g(x) \to C_\pm \) as \(x\to \pm \infty \), { (ii)} \( g'\in H^s\) for some \(s\geq 0\), { (iii)} \( (g-C_+)\in L^2(0,\infty)\), \((g-C_-)\in L^2(-\infty ,0)\). Similar conclusions are derived for the solutions of the Benjamin-Ono (BO) equation.

Reviewer: Milan Štědrý (Praha)

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35G25	Initial value problems for nonlinear higher-order PDEs

Keywords:

Korteweg-de Vries equation; Benjamin-Ono equation; global well-posedness; bore-like initial data