基于预解式估计的变漂移场双速模型指数收敛于平衡点
Exponential convergence to equilibrium for a two-speed model with variant drift fields via the resolvent estimate
摘要：
本文研究了一个具有不同漂移场的双速模型，它推广了Goldstein-Taylor模型，但两个平流场不一定成比例。由于缺乏一个局部平衡结构的稳定状态，流行的hypovigality方法不能直接应用于这样的系统。为了证明这个模型的指数收敛到平衡点，我们使用最近推广的Gearhart-Prüss定理[Sci. China Math.64（2021），no.3，507-518]以获得半群界，其中相对熵估计在经由紧性论证获得期望的预解式估计中起核心作用。
英文摘要：
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack of a local equilibrium structure of the steady state, prevailing hypocoercivity methods could not be directly applied to such a system. To prove the exponential convergence to equilibrium for this model, we use a recent generalization of the Gearhart-Prüss theorem [Sci. China Math. 64 (2021), no. 3, 507-518] to gain semigroup bounds, where the relative entropy estimate plays a central role in gaining desired resolvent estimates via a compactness argument.
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