Well-posedness results for the 3D Zakharov-Kuznetsov equation

Francis Ribaud (1) , Stéphane Vento (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$. The proof is based on a sharp maximal function estimate in time-weighted spaces.

Mots clés: KdV-like equations; Cauchy problem

Domaines: Equations aux dérivées partielles [math.AP]

Francis Ribaud, Stéphane Vento. Well-posedness results for the 3D Zakharov-Kuznetsov equation. 2011. ⟨hal-00640272⟩