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PreprintCC BY-NC-ND 4.0arXiv

Uniqueness of the dissipative SQG without time-continuity assumption

  • Taiki Okazaki
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Abstract

We consider the uniqueness of the solution of the dissipative surface quasi-geostrophic equation, without assuming time-continuity and smallness of the solutions. We show that the uniqueness holds in the scale-critical Lebesgue spaces and non-homogeneous Besov spaces. The proof is based on the energy method, inspired by the approach introduced by Lions and Masmoudi (2001) in the study of uniqueness for the Navier-Stokes equations. A key ingredient of the argument is the justification of the energy inequality via the smoothing effect of the fractional heat semigroup together with an iteration scheme based on the structure of the integral equation.

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Cite

BibTeXRIS
BibTeX
@misc{okazaki2026uniqueness,
  title = {{Uniqueness of the dissipative SQG without time-continuity assumption}},
  author = {Taiki Okazaki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.13065},
  eprint = {2606.13065},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.13065},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Uniqueness of the dissipative SQG without time-continuity assumption
AU  - Taiki Okazaki
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2606.13065
UR  - https://arxiv.org/abs/2606.13065
AB  - We consider the uniqueness of the solution of the dissipative surface quasi-geostrophic equation, without assuming time-continuity and smallness of the solutions. We show that the uniqueness holds in the scale-critical Lebesgue spaces and non-homogeneous Besov spaces. The proof is based on the energy method, inspired by the approach introduced by Lions and Masmoudi (2001) in the study of uniqueness for the Navier-Stokes equations. A key ingredient of the argument is the justification of the energy inequality via the smoothing effect of the fractional heat semigroup together with an iteration scheme based on the structure of the integral equation.
ER  -