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Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise

  • Abhishek Chaudhary
  • Ujjwal Koley
  • Andreas Prohl
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Abstract

We study a fully discrete approximation theory for the two-dimensional incompressible Euler equations on ๐•‹2, in vorticity form, driven by Kraichnan-type transport noise and with โ„โˆ’1(๐•‹2)-valued initial vorticity. The main new ingredient is a finite-dimensional coercivity estimate for the torus Kraichnan model, which captures at the discrete level the regularizing mechanism induced by the rough transport noise. Together with a new compactness strategy based on continuous equation-based interpolants and localized discrete estimates, this coercivity estimate gives tightness of the approximations and shows that subsequential limit is a weak martingale solution of the Euler equations.

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Cite

BibTeXRIS
BibTeX
@misc{chaudhary2026convergence,
  title = {{Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise}},
  author = {Abhishek Chaudhary and Ujjwal Koley and Andreas Prohl},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31369},
  eprint = {2609.31369},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31369},
}
RIS
TY  - UNPB
TI  - Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise
AU  - Abhishek Chaudhary
AU  - Ujjwal Koley
AU  - Andreas Prohl
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31369
UR  - https://arxiv.org/abs/2609.31369
AB  - We study a fully discrete approximation theory for the two-dimensional incompressible Euler equations on ๐•‹^2, in vorticity form, driven by Kraichnan-type transport noise and with โ„^โˆ’1(๐•‹^2)-valued initial vorticity. The main new ingredient is a finite-dimensional coercivity estimate for the torus Kraichnan model, which captures at the discrete level the regularizing mechanism induced by the rough transport noise. Together with a new compactness strategy based on continuous equation-based interpolants and localized discrete estimates, this coercivity estimate gives tightness of the approximations and shows that subsequential limit is a weak martingale solution of the Euler equations.
ER  -