Large deviation principles for 2D stochastic g-Navier--Stokes equations on unbounded channel-like domains
Abstract
This paper investigates the large deviation principle for 2D stochastic g-Navier--Stokes equations driven by multiplicative noise and defined on an unbounded channel-like domain. We first prove the existence and uniqueness of probabilistically strong solutions for the stochastic equation under small noise perturbations by means of the local monotonicity method. Subsequently, we show the well-posedness of solutions to the corresponding control equation and the convergence in distribution of the solutions for the stochastic equation as the noise intensity tends to zero. Finally, we establish the Freidlin-Wentzell type large deviation principle for the solutions of the stochastic equation by using the weak convergence method. To overcome the lack of compactness of Sobolev embedding on unbounded domains, we employ a scalar stream function together with a truncation technique to derive uniform tail estimates for the solutions of the control equation.
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BibTeX
@misc{he2026large,
title = {{Large deviation principles for 2D stochastic $g$-Navier--Stokes equations on unbounded channel-like domains}},
author = {Gang He and Ji Shu and Huixia Wen and Longyu Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16381},
eprint = {2610.16381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16381},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large deviation principles for 2D stochastic g-Navier--Stokes equations on unbounded channel-like domains
AU - Gang He
AU - Ji Shu
AU - Huixia Wen
AU - Longyu Wu
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16381
UR - https://arxiv.org/abs/2610.16381
AB - This paper investigates the large deviation principle for 2D stochastic g-Navier--Stokes equations driven by multiplicative noise and defined on an unbounded channel-like domain. We first prove the existence and uniqueness of probabilistically strong solutions for the stochastic equation under small noise perturbations by means of the local monotonicity method. Subsequently, we show the well-posedness of solutions to the corresponding control equation and the convergence in distribution of the solutions for the stochastic equation as the noise intensity tends to zero. Finally, we establish the Freidlin-Wentzell type large deviation principle for the solutions of the stochastic equation by using the weak convergence method. To overcome the lack of compactness of Sobolev embedding on unbounded domains, we employ a scalar stream function together with a truncation technique to derive uniform tail estimates for the solutions of the control equation.
ER -