全直线上随机粘性守恒律方程的多项式混合
Polynomial mixing for stochastic viscous conservation law equation on the whole line
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中文总结 AI 辅助
该研究针对全直线上受时空白噪声力及小阻尼、粘性的随机粘性守恒律方程，基于抽象多项式耦合准则和Foiaş--Prodi估计，在两类情形下建立多项式混合率，为相关方程的长时间行为分析提供了理论依据。
中文摘要 AI 辅助
本文研究全实直线上的粘性守恒律方程在受到时空白噪声力及任意小阻尼、粘性常数作用下的长时间行为。我们在两种情形下建立了多项式混合率：(a) 带超粘性耗散的一般超二次通量，其中非线性项的增长由超粘性的阶数控制，且力在一般L²基上充分非退化；(b) 带标准二阶耗散的一般二次通量，且力在某个无条件基上非退化。两种情形均包含经典的Burgers型非线性项。证明基于arXiv:2408.00592中提出的抽象多项式耦合准则及Foiaş--Prodi估计。
英文摘要
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.
发表机构
- School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University（东北师范大学数学与统计学院、数学与交叉科学中心）
- Department of Mathematics, Southern University of Science and Technology（南方科技大学数学系）
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