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PreprintCC BY 4.0arXiv

Subcritical non-linear heat equations via spectral gap

  • Ilya Chevyrev
  • Hora Mirsajjadi
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Abstract

We establish local well-posedness for a class of non-linear heat equations on the torus 𝕋n whose highest order non-linearities have scaling-critical dimension −1/k, k∈ ℕ, when the initial condition is a random field satisfying a spectral gap inequality involving a suitable Lebesgue norm. The corresponding subcriticality condition matches that of the Gaussian free field in dimension d<2+2/k. This extends previous subcritical well-posedness results beyond the Gaussian setting. Moreover, our proof is simpler and avoids diagrammatic arguments.

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Cite

BibTeXRIS
BibTeX
@misc{chevyrev2026subcritical,
  title = {{Subcritical non-linear heat equations via spectral gap}},
  author = {Ilya Chevyrev and Hora Mirsajjadi},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28317},
  eprint = {2608.28317},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28317},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Subcritical non-linear heat equations via spectral gap
AU  - Ilya Chevyrev
AU  - Hora Mirsajjadi
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28317
UR  - https://arxiv.org/abs/2608.28317
AB  - We establish local well-posedness for a class of non-linear heat equations on the torus 𝕋^n whose highest order non-linearities have scaling-critical dimension −1/k, k∈ ℕ, when the initial condition is a random field satisfying a spectral gap inequality involving a suitable Lebesgue norm. The corresponding subcriticality condition matches that of the Gaussian free field in dimension d<2+2/k. This extends previous subcritical well-posedness results beyond the Gaussian setting. Moreover, our proof is simpler and avoids diagrammatic arguments.
ER  -