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ON THE PERSISTENCE PROPERTIES OF SOLUTIONS OF NONLINEAR DISPERSIVE EQUATIONS IN WEIGHTED
 

Summary: ON THE PERSISTENCE PROPERTIES OF SOLUTIONS OF
NONLINEAR DISPERSIVE EQUATIONS IN WEIGHTED
SOBOLEV SPACES
J. NAHAS AND G. PONCE
Abstract. We study persistence properties of solutions to some canonical dis-
persive models, namely the semi-linear Schršodinger equation, the k-generalized
Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev
spaces Hs(Rn) L2(|x|ldx), s, l > 0.
1. Introduction
This work is concerned with persistence properties of solutions to some nonlinear
dispersive equations in weighted Sobolev spaces Hs
(Rn
) L2
(|x|l
dx), s, l > 0. We
shall consider the initial value problems (IVP) associated to the following dispersive
models : the nonlinear Schršodinger (NLS) equation
(1.1) itu + u = ”|u|a-1
u, t R, x Rn
, ” = ±1, a > 1,

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics