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Interfaces and Free Boundaries


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Volume 20, Issue 4, 2018, pp. 533–550
DOI: 10.4171/IFB/411

Published online: 2018-12-13

Asymptotic stability of local Helfrich minimizers

Daniel Lengeler[1]

(1) Universität Regensburg, Germany

We show that local minimizers of the Canham–Helfrich energy are asymptotically stable with respect to a model for relaxational fluid vesicle dynamics that we already studied in previous papers ([13, 14]). The proof is based on a Łojasiewicz–Simon inequality.

Keywords: Willmore energy, Canham–Helfrich energy, gradient flow, geometric flow,Willmore flow, Helfrich flow, Helfrich equation, Stokes system, linear elliptic system, fluid dynamics, biological membrane, lipid bilayer, well-posedness, stability

Lengeler Daniel: Asymptotic stability of local Helfrich minimizers. Interfaces Free Bound. 20 (2018), 533-550. doi: 10.4171/IFB/411