Fronts internes de grandes amplitudes pour des systèmes à deux fluides

Translated title of the contribution: Large-amplitude internal fronts in two-fluid systems

Robin Ming Chen, Samuel Walsh, Miles H. Wheeler

Research output: Contribution to journalArticlepeer-review

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.

Translated title of the contributionLarge-amplitude internal fronts in two-fluid systems
Original languageFrench
Pages (from-to)1073-1083
Number of pages11
JournalComptes Rendus Mathematique
Volume358
Issue number9
DOIs
Publication statusPublished - 5 Jan 2021

ASJC Scopus subject areas

  • Mathematics(all)

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