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arXiv · 2609.18185

Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations

Honglei Chen·Zhenxin Liu
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Abstract

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 $\var\to0$ 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 $\var\to0$ 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.

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Honglei Chen, Zhenxin Liu. 2026-09-16. Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations. https://arxiv.org/abs/2609.18185

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