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PreprintCC BY 4.0arXiv

Dynamical stability for the periodic modified Mullins-Sekerka flow

  • Daniele De Gennaro
  • Anna Kubin
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Abstract

We prove dynamical stability in arbitrary dimension for the modified Mullins--Sekerka flow, the gradient flow of the sharp-interface Ohta--Kawasaki energy on the flat torus. Specifically, we show that if an initial set has the same volume as a strictly stable critical set for the energy and is sufficiently close to it in C3,α, then the flow exists for all times and converges exponentially fast, in every Ck norm, to a translate of that critical set. The proof relies on a quantitative Alexandrov-type estimate for strictly stable critical sets of the energy.

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Cite

BibTeXRIS
BibTeX
@misc{gennaro2026dynamical,
  title = {{Dynamical stability for the periodic modified Mullins-Sekerka flow}},
  author = {Daniele De Gennaro and Anna Kubin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37201},
  eprint = {2609.37201},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37201},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dynamical stability for the periodic modified Mullins-Sekerka flow
AU  - Daniele De Gennaro
AU  - Anna Kubin
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37201
UR  - https://arxiv.org/abs/2609.37201
AB  - We prove dynamical stability in arbitrary dimension for the modified Mullins--Sekerka flow, the gradient flow of the sharp-interface Ohta--Kawasaki energy on the flat torus. Specifically, we show that if an initial set has the same volume as a strictly stable critical set for the energy and is sufficiently close to it in C^3,α, then the flow exists for all times and converges exponentially fast, in every C^k norm, to a translate of that critical set. The proof relies on a quantitative Alexandrov-type estimate for strictly stable critical sets of the energy.
ER  -