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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 Foiaş--Prodi estimate.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026polynomial,
  title = {{Polynomial mixing for stochastic viscous conservation law equation on the whole line}},
  author = {Peng Gao and Liying Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.29824},
  eprint = {2608.29824},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29824},
}
RIS
TY  - UNPB
TI  - Polynomial mixing for stochastic viscous conservation law equation on the whole line
AU  - Peng Gao
AU  - Liying Li
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.29824
UR  - https://arxiv.org/abs/2608.29824
AB  - 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 Foiaş--Prodi estimate.
ER  -