A class on non-local linear operators for vorticity waves

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

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Filipe Oliveira *

E-mail: [email protected]