Polynomial mixing for stochastic viscous conservation law equation on the whole line

Peng Gao; Liying Li

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arXiv · 2608.29824

Polynomial mixing for stochastic viscous conservation law equation on the whole line

Peng Gao·Liying Li

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Abstract

In this paper, we study the long-time behavior of the viscous conservation law equation on the whole real line, subject to a white-in-time force and arbitrarily small damping and viscosity constants. We establish polynomial mixing rates in two settings: (a) a general super-quadratic flux with hyperviscous dissipation, where the growth of the nonlinearity is controlled by the order of hyperviscosity, and the force is sufficiently non-degenerate on a generic L2-basis; and (b) a general quadratic flux with standard second-order dissipation, and the force is non-degenerate on some unconditional basis. Both settings include the classical Burgers-type nonlinearity. The proof is based on an abstract polynomial coupling criterion developed in arXiv:2408.00592 and a Foia\c{s}--Prodi estimate.

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Peng Gao, Liying Li. 2026-08-30. Polynomial mixing for stochastic viscous conservation law equation on the whole line. https://arxiv.org/abs/2608.29824

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