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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.
- 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