Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise

Chang Liu; Dejun Luo

Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise

Probability 2025-01-22 v2

Authors: Chang Liu , Dejun Luo

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.

Keywords

stochastic Navier-Stokes equations transport noise scaling limit large deviation global modification hyperviscosity

Cite

@article{arxiv.2412.20752,
  title  = {Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise},
  author = {Chang Liu and Dejun Luo},
  journal= {arXiv preprint arXiv:2412.20752},
  year   = {2025}
}

Comments

36 pages. We slightly modified the proof of Lemma 4.1 and some other typos

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