A class on non-local linear operators for vorticity waves

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...

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Published inApplicable analysis Vol. 84; no. 12; pp. 1287 - 1302
Main Author Oliveira, Filipe
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.12.2005
Subjects
AMS Subject Classifications: 47G00
Oscillatory integrals
Strichartz estimates
Vorticity waves
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ISSN0003-6811
1563-504X
DOI10.1080/00036810412331282952

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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.
AbstractList 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 'Lp-Lq' and Strichartz-type estimates for the solutions of the linearized equations.
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.
Author Oliveira, Filipe
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Cites_doi 10.1017/S0022112096008282
10.57262/die/1367265625
10.1512/iumj.1991.40.40003
10.1090/S0002-9904-1975-13790-6
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References Stein EM (bib7) 1993
bib8
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Olver Frank (bib4) 1974
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– volume: 12
  start-page: 137
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– volume-title: Introduction to Fourier Analysis in Euclidian Space
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  ident: bib2
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  doi: 10.1090/S0002-9904-1975-13790-6
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Snippet A steady longitudinal current in the nearshore can, in some conditions, support oscillations known as vorticity waves or shear waves. In this article, we...
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SubjectTerms AMS Subject Classifications: 47G00
Oscillatory integrals
Strichartz estimates
Vorticity waves
Title A class on non-local linear operators for vorticity waves
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