Orbital stability for internal waves

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Robin Ming Chen
October 18, 2021
10:20AM - 11:20AM
Location
Zoom

Date Range
Add to Calendar 2021-10-18 10:20:00 2021-10-18 11:20:00 Orbital stability for internal waves Title:  Orbital stability for internal waves Speaker:  Robin Ming Chen (University of Pittsburgh) Speaker's URL:  https://sites.pitt.edu/~mingchen/ Abstract:  I will discuss the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler equations, with the density of each fluid being constant but distinct. We prove that for supercritical surface tension, all known small-amplitude localized waves are (conditionally) orbitally stable in the natural energy space. Moreover, the trivial solution is shown to be conditionally stable when the Bond and Froude numbers lie in a certain unbounded parameter region. For the near critical surface tension regime, we show that one can infer conditional orbital stability or orbital instability of small-amplitude traveling waves solutions to the full Euler system from considerations of a dispersive PDE similar to the steady Kawahara equation. This is joint work with S. Walsh. URL associated with Seminar https://research.math.osu.edu/pde/ Zoom link (the same zoom link for other PDE seminars): https://osu.zoom.us/j/93517408580?pwd=M1dlWXo1L3oyYXZhY2JFdHRiV0JGQT09 Meeting ID: 935 1740 8580 Password: 314159 Zoom Department of Mathematics math@osu.edu America/New_York public
Description

Title:  Orbital stability for internal waves

Speaker:  Robin Ming Chen (University of Pittsburgh)

Speaker's URL:  https://sites.pitt.edu/~mingchen/

Abstract:  I will discuss the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler equations, with the density of each fluid being constant but distinct. We prove that for supercritical surface tension, all known small-amplitude localized waves are (conditionally) orbitally stable in the natural energy space. Moreover, the trivial solution is shown to be conditionally stable when the Bond and Froude numbers lie in a certain unbounded parameter region. For the near critical surface tension regime, we show that one can infer conditional orbital stability or orbital instability of small-amplitude traveling waves solutions to the full Euler system from considerations of a dispersive PDE similar to the steady Kawahara equation. This is joint work with S. Walsh.

URL associated with Seminar
https://research.math.osu.edu/pde/

Zoom link (the same zoom link for other PDE seminars): https://osu.zoom.us/j/93517408580?pwd=M1dlWXo1L3oyYXZhY2JFdHRiV0JGQT09

Meeting ID: 935 1740 8580 Password: 314159

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