A class on non-local linear operators for vorticity waves

Author: Oliveira, Filipe

Source: Applicable Analysis, Volume 84, Number 12, December 2005 , pp. 1287-1302(16)

Buy & download fulltext article:

Price: $56.94 plus tax (Refund Policy)

Abstract:

A steady longitudinal current in the nearshore can, in some conditions, support oscillations known as vorticity waves or shear waves. In this article, we consider a family of nonlinear evolution equations derived by Shrira and Voronovitch to describe the dynamics of vorticity waves near the coastal line and make the study of the dispersion and smoothing properties of the associated nonlocal free problems. More precisely, after establishing long and short time uniform estimates for a certain class of oscillatory integrals, we derive “ L p - L q ” and Strichartz-type estimates for the solutions of the linearized equations.

Keywords: Vorticity waves; Oscillatory integrals; Strichartz estimates; AMS Subject Classifications: 47G00; 35Q53; 35Q35

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810412331282952

Affiliations: 1: Communicated by A. Jeffrey

Publication date: 2005-12-01

More about this publication?