▪ Abstract This review deals primarily with the bifurcation, stability, and evolution of gravity
and capillary-gravity waves. Recent results on the bifurcation of various types of capillary …

The problem of turbulence is one of the central problems in theoretical physics. While the
theory of fully developed turbulence has been widely studied, the theory of wave turbulence …

This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

We prove the existence and the linear stability of Cantor families of small amplitude time
quasi-periodic standing water wave solutions—namely periodic and even in the space …

arXiv:0901.3261v1 [math.PR] 21 Jan 2009 Page 1 arXiv:0901.3261v1 [math.PR] 21 Jan 2009
FROM THE LONG JUMP RANDOM WALK TO THE FRACTIONAL LAPLACIAN ENRICO …

We consider the gravity water waves system in the case of a one dimensional interface, for
sufficiently smooth and localized initial data, and prove global existence of small solutions …

We consider the question of global existence of small, smooth, and localized solutions of a
certain fractional semilinear cubic NLS in one dimension, i∂ tu− Λ u= c 0| u| 2 u+ c 1 u 3+ c …

We prove the existence and the linear stability of small amplitude time quasi-periodic
standing wave solutions (ie periodic and even in the space variable $ x $) of a $2 …

The goal of this monograph is to prove that any solution of the Cauchy problem for the
capillary-gravity water waves equations, in one space dimension, with periodic, even in …