This paper is concerned with the Cauchy problem of the 2D Zakharov-Kuznetsov equation.
We prove bilinear estimates which imply local in time well-posedness in the Sobolev space …

Uniform L 2-estimates for the convolution of singular measures with respect to transversal
submanifolds are proved in arbitrary space dimension. The results of Bennett–Bez are used …

We prove that the best constant in the general Brascamp-Lieb inequality is a locally
bounded function of the underlying linear transformations. As applications we deduce …

We prove a nonlinear variant of the general Brascamp–Lieb inequality. Our proof consists of
running an efficient, or “tight,” induction-on-scales argument, which uses the existence of …

We construct approximate solutions $(\psi_*, n_*) $ of the critical 4D Zakharov system which
collapse in finite time to a singular renormalization of the solitary bulk solutions $(\lambda …

The purpose of this article is to survey certain aspects of multilinear harmonic analysis
related to notions of transversality. Particular emphasis will be placed on the multilinear …

arXiv:1203.3959v3 [math.AP] 23 Jan 2013 Page 1 arXiv:1203.3959v3 [math.AP] 23 Jan 2013
SMALL ENERGY SCATTERING FOR THE ZAKHAROV SYSTEM WITH RADIAL SYMMETRY …

We consider the Zakharov system with periodic boundary conditions in dimension one. In
the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the …

We prove global existence and scattering for small localized solutions of the Cauchy
problem for the Zakharov system in 3 space dimensions. The wave component is shown to …

The Zakharov-Kuznetsov equation in space dimension $ d\geq 3$ is considered. It is proved
that the Cauchy problem is locally well-posed in $ H^ s (\mathbb {R}^ d) $ in the full …