Time-periodic oscillation of capillary fluid droplet
Chengyang Shao1 ; Haocheng Yang1
1Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France
Séminaire Laurent Schwartz — EDP et applications (2025), Exposé no. 15, 17 p.

In this note, we outline the construction of time-periodic oscillating capillary fluid droplet, based on a working paper of the authors. The droplet is modeled by an incompressible, irrotational Eulerian system with free boundary. The key tool developed in the research work is a coordinate-free paradifferential calculus on the compact Lie group $\mathrm{SU}(2)$, together with its zonal version. The Eulerian free boundary system is paralinearized into a quasilinear dispersive PDE. Despite the presence of small denominators, paradifferential reduction allows one to rewrite the system into a fixed point form balancing all loss of regularity. The construction of time-periodic solutions is then based on bifurcation theory with computer assistance.

Publié le :
DOI : 10.5802/slsedp.190

Chengyang Shao  1   ; Haocheng Yang  1

1 Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France 
Chengyang Shao; Haocheng Yang. Time-periodic oscillation of capillary fluid droplet. Séminaire Laurent Schwartz — EDP et applications (2025), Exposé no. 15, 17 p.. doi: 10.5802/slsedp.190
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