Steady bubbles and drops in inviscid fluidsOpen Access

Meyer, David; Niebel, Lukas; Seis, Christian

Forschungsartikel (Zeitschrift) | Peer reviewed

Zusammenfassung

We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a bounded connected domain. The solutions have a uniform vorticity distribution in this inner phase and they have a vortex sheet on its surface. Our construction relies on a perturbative approach around an explicit spherical solution, given by Hill’s vortex enclosed by a spherical vortex sheet. The construction is sensitive to the Weber numbers describing the flow. At critical Weber numbers, we perform a bifurcation analysis utilizing the Crandall–Rabinowitz theorem in Sobolev spaces on the 2-sphere. Away from these critical numbers, our construction relies on the implicit function theorem. Our results imply that the model containing surface tension is richer than the ordinary one-phase Euler equations, in the sense that for the latter, Hill’s spherical vortex is unique (modulo translations) among all axisymmetric simply connected uniform vortices of a given circulation.

Details zur Publikation

FachzeitschriftCalculus of Variations and Partial Differential Equations
Jahrgang / Bandnr. / Volume64
Ausgabe / Heftnr. / Issue299
StatusVeröffentlicht
Veröffentlichungsjahr2025
Sprache, in der die Publikation verfasst istEnglisch
DOI10.1007/s00526-025-03144-w
Link zum Volltexthttps://link.springer.com/article/10.1007/s00526-025-03144-w
Stichwörtertwo-phase Euler equations; bubbles; droplets; traveling wave solutions; overdetermined boundary value problem; Hill's vortex

Autor*innen der Universität Münster

Seis, Christian
Professur für Angewandte Mathematik (Prof. Seis)