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PreprintCC BY 4.0arXiv

The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow

  • Yuning Liu
  • Yoshihiro Tonegawa
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Abstract

We study the sharp-interface limit of the two-dimensional incompressible Navier--Stokes/Allen--Cahn system with constant mobility and prove the existence of global integral varifold solutions to the coupled Navier--Stokes/mean curvature flow system. The limiting interface measure satisfies Brakke's inequality, and its normal velocity equals the sum of its mean curvature and the normal projection of the fluid velocity.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026sharp,
  title = {{The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow}},
  author = {Yuning Liu and Yoshihiro Tonegawa},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04631},
  eprint = {2611.04631},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04631},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Sharp Interface Limit of the Two-Dimensional Navier--Stokes/Allen--Cahn System as a Brakke Flow
AU  - Yuning Liu
AU  - Yoshihiro Tonegawa
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04631
UR  - https://arxiv.org/abs/2611.04631
AB  - We study the sharp-interface limit of the two-dimensional incompressible Navier--Stokes/Allen--Cahn system with constant mobility and prove the existence of global integral varifold solutions to the coupled Navier--Stokes/mean curvature flow system. The limiting interface measure satisfies Brakke's inequality, and its normal velocity equals the sum of its mean curvature and the normal projection of the fluid velocity.
ER  -