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Scaling limit and large deviation for 3D globally modified stochastic Navier–Stokes equations with transport noise

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  • Liu, Chang
  • Luo, Dejun

Abstract

We consider the globally modified stochastic (hyperviscous) Navier–Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of the weak solutions, and then show their convergence to the solutions of the deterministic 3D globally modified (hyperviscous) Navier–Stokes equations in an appropriate scaling limit. Furthermore, we prove a large deviation principle for the stochastic globally modified hyperviscous system.

Suggested Citation

  • Liu, Chang & Luo, Dejun, 2026. "Scaling limit and large deviation for 3D globally modified stochastic Navier–Stokes equations with transport noise," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002145
    DOI: 10.1016/j.spa.2025.104770
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    References listed on IDEAS

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    1. Luo, Dejun, 2011. "Absolute continuity under flows generated by SDE with measurable drift coefficients," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2393-2415, October.
    2. Flandoli, F. & Gubinelli, M. & Priola, E., 2011. "Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1445-1463, July.
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