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Energy estimates and local well-posedness of 3D interfacial hydroelastic waves between two incompressible fluids.

Energy estimates and local well-posedness of 3D interfacial hydroelastic waves between two incompressible fluids.

Authors :
Wang, Zhan
Yang, Jiaqi
Source :
Journal of Differential Equations. Sep2020, Vol. 269 Issue 7, p6055-6087. 33p.
Publication Year :
2020

Abstract

In the current paper, we are concerned with waves propagating through the deformation of a thin elastic sheet between two incompressible and inviscid fluids, which are usually called hydroelastic waves in the literature to model deformable sheets interacting with surrounding fluids. The main purpose of the present study is to solve a basic question on the theoretical side, i.e. the local well-posedness issue. The problem is formulated by the full Euler equations (without the assumption of irrotationality) for fluids, combined with the Plotnikov-Toland model for the elastic sheet. Based on geometric considerations, we derive energy estimates and prove the local existence and uniqueness of solution for this system in n (⩾ 2) dimensions even if velocity fields are rotational. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00220396
Volume :
269
Issue :
7
Database :
Academic Search Index
Journal :
Journal of Differential Equations
Publication Type :
Academic Journal
Accession number :
143495823
Full Text :
https://doi.org/10.1016/j.jde.2020.04.029