Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations
Abstract
We establish three weak averaging principles for distribution-dependent stochastic Navier--Stokes equations with rapidly oscillating coefficients on the torus T2. First, solution laws are relatively compact on finite time intervals, and every limit point as var→0 is the path law of a variational martingale solution of the averaged equation. Under a dissipative condition, we can choose bounded complete variational solution laws of the original and averaged equations so that every sequence with var→0 has a subsequence converging weakly to a bounded complete variational solution law of the averaged equation. At the level of probability laws, the original nonautonomous equation admits a family of weak pullback attractors, while the averaged equation has a weak global attractor. The weak pullback attractors converge upper semicontinuously to the weak global attractor of the averaged equation, uniformly with respect to the coefficient hull.
Related
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BibTeX
@misc{chen2026weak,
title = {{Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations}},
author = {Honglei Chen and Zhenxin Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18185},
eprint = {2609.18185},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18185},
}
RIS
TY - UNPB
TI - Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations
AU - Honglei Chen
AU - Zhenxin Liu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18185
UR - https://arxiv.org/abs/2609.18185
AB - We establish three weak averaging principles for distribution-dependent stochastic Navier--Stokes equations with rapidly oscillating coefficients on the torus T^2. First, solution laws are relatively compact on finite time intervals, and every limit point as var→0 is the path law of a variational martingale solution of the averaged equation. Under a dissipative condition, we can choose bounded complete variational solution laws of the original and averaged equations so that every sequence with var→0 has a subsequence converging weakly to a bounded complete variational solution law of the averaged equation. At the level of probability laws, the original nonautonomous equation admits a family of weak pullback attractors, while the averaged equation has a weak global attractor. The weak pullback attractors converge upper semicontinuously to the weak global attractor of the averaged equation, uniformly with respect to the coefficient hull.
ER -