Large-time existence for one-dimensional Green-Naghdi equations with vorticity

Colette Guillopé; Samer Israwi; Raafat Talhouk

doi:10.3934/dcdss.2021040

Article Contents

2021, Volume 14, Issue 8: 2947-2974. Doi: 10.3934/dcdss.2021040

This issue Previous Article Global attractor for damped forced nonlinear logarithmic Schrödinger equations Next Article Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound

Large-time existence for one-dimensional Green-Naghdi equations with vorticity

1.
LAMA, Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, F-94010, Créteil, France
2.
Mathématiques, Faculté des sciences I et Laboratoire de mathématiques, École doctorale des sciences et technologie, Université Libanaise, Beyrouth, Liban

^* Corresponding author: Raafat Talhouk
^* Corresponding author: Raafat Talhouk

Received: May 31, 2020

Revised: February 28, 2021

Early access: April 2021

Published: August 2021

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Abstract

This essay is concerned with the one-dimensional Green-Naghdi equations in the presence of a non-zero vorticity according to the derivation in [5], and with the addition of a small surface tension. The Green-Naghdi system is first rewritten as an equivalent system by using an adequate change of unknowns. We show that solutions to this model may be obtained by a standard Picard iterative scheme. No loss of regularity is involved with respect to the initial data. Moreover solutions exist at the same level of regularity as for first order hyperbolic symmetric systems, i.e. with a regularity in Sobolev spaces of order $ s>3/2 $.

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Mathematics Subject Classification: 76B15, 35A01, 35Q35.

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