Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension

Abstract : In this paper, we will derive the two-dimensional extended Green-Naghdi system {see Matsuno [Proc. R. Soc. A 472, 20160127 (2016)] for determination in a various way} for flat bottoms of order three with respect to the shallowness parameter μ. Then we consider the 1D extended Green-Naghdi equations taking into account the effect of small surface tension. We show that the construction of solution with a standard Picard iterative scheme can be accomplished in which the well-posedness in Xs=Hs+2(ℝ)×Hs+2(ℝ) for some s>32 of the new extended 1D system for a finite large time existence t=O(1ε) is demonstrated.
Document type :
Journal articles
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02202795
Contributor : Samer Israwi <>
Submitted on : Wednesday, July 31, 2019 - 5:27:16 PM
Last modification on : Friday, August 2, 2019 - 1:18:40 AM

File

Derivation and Well-posedness ...
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Bashar Khorbatly, Ibtissam Zaiter, Samer Israwi. Derivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tension. Journal of Mathematical Physics, American Institute of Physics (AIP), 2018, 59 (7), pp.071501. ⟨10.1063/1.5020601⟩. ⟨hal-02202795⟩

Share

Metrics

Record views

6

Files downloads

6