Skip to Main content Skip to Navigation
Journal articles

Bilinear Strichartz estimates for the ZK equation and applications

Abstract : We prove that the associated initial value problem is locally well-posed in $H^s(\mathbb R^2)$ for $s>\frac12$ and globally well-posed in $H^1(\mathbb R\times \mathbb T)$ and in $H^s(\R^3) $ for $ s>1$. Our main new ingredient is a bilinear Strichartz estimate in the context of Bourgain's spaces which allows to control the high-low frequency interactions appearing in the nonlinearity of \eqref{ZK0}. In the $\mathbb R^2$ case, we also need to use a recent result by Carbery, Kenig and Ziesler on sharp Strichartz estimates for homogeneous dispersive operators. Finally, to prove the global well-posedness result in $ \R^3 $, we need to use the atomic spaces introduced by Koch and Tataru.
Document type :
Journal articles
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download
Contributor : Luc Molinet Connect in order to contact the contributor
Submitted on : Monday, September 28, 2015 - 11:55:58 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Tuesday, December 29, 2015 - 10:22:11 AM


LWP ZK (final 26-03-13).pdf
Files produced by the author(s)


  • HAL Id : hal-01205993, version 1



Luc Molinet, Didier Pilod. Bilinear Strichartz estimates for the ZK equation and applications. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2015, 32 (2), pp.347-371. ⟨hal-01205993⟩



Record views


Files downloads