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Large-amplitude internal fronts in two-fluid systems
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incompressible Euler equation in two dimensions. The fluids are bounded above and below by flat horizontal walls and acted upon by gravity. We obtain continuous curves of solutions to this system that bifurcate from the trivial solution where the interface is flat. Following these families to the their extreme, the internal interface either overturns, comes into contact with the upper wall, or develops a highly degenerate "double stagnation" point. Our construction is made possible by a new abstract machinery for global continuation of monotone front-type solutions to elliptic equations posed on infinite cylinders. This theory is quite robust and, in particular, can treat fully nonlinear equations as well as quasilinear problems with transmission boundary conditions.<br />Comment: This is a shorter description of results first appearing in arXiv:2005.00651 with additional motivation and connections to modeling
- Subjects :
- General Mathematics
010102 general mathematics
Degenerate energy levels
Mathematical analysis
Front (oceanography)
01 natural sciences
Euler equations
Nonlinear system
symbols.namesake
35B32, 76B15, 35J60, 35J66
Mathematics - Analysis of PDEs
Amplitude
Monotone polygon
0103 physical sciences
Compressibility
symbols
FOS: Mathematics
010307 mathematical physics
Boundary value problem
0101 mathematics
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....44904c7bb4461a518eefa89681c58760
- Full Text :
- https://doi.org/10.48550/arxiv.2007.16055