On well-posedness for the Benjamin-Ono equation

N. Burq (1) , F. Planchon (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove existence of solutions for the Benjamin-Ono equation with data in $H^s(\R)$, $s>0$. Thanks to conservation laws, this yields global solutions for $H^\frac 1 2(\R)$ data, which is the natural ``finite energy'' class. Moreover, inconditional uniqueness is obtained in $L^\infty_t(H^\frac 1 2(\R))$, which includes weak solutions, while for $s>\frac 3 {20}$, uniqueness holds in a natural space which includes the obtained solutions.

Domaines: Equations aux dérivées partielles [math.AP]

N. Burq, F. Planchon. On well-posedness for the Benjamin-Ono equation. 2005. ⟨hal-00017561⟩