Abstract : We consider an overdetermined elliptic problem known as the hollow vortex problem. We prove that the solutions to this problem are in 1:1 correspondence with minimal graphs bounded by horizontal symmetry lines. We use this correspondence to give various examples of domains with hollow vortices.
https://hal.archives-ouvertes.fr/hal-01270166
Contributor : Martin Traizet <>
Submitted on : Friday, February 5, 2016 - 5:43:05 PM Last modification on : Friday, February 19, 2021 - 4:10:03 PM Long-term archiving on: : Saturday, November 12, 2016 - 12:36:20 PM
Martin Traizet. Hollow vortices and minimal surfaces. Journal of Mathematical Physics, American Institute of Physics (AIP), 2015, 56, pp.083101. ⟨10.1063/1.4927248⟩. ⟨hal-01270166⟩