报告题目：Uniqueness of Invariant Measures for Stochastic Damped Anisotropic Navier–Stokes Equations on the Whole Plane

报 告 人：梁思玉 讲师（南京理工大学）

报告时间：2026年6月15日（星期一）14：00-15：00

报告地点：数学科学学院114（小报告厅）  

校内联系人： 程梦雨 副教授   联系方式：84708351-8206

报告摘要：This talk concerns the long-time behavior of a two-dimensional stochastic anisotropic Navier–Stokes equation on the whole plane R^2, with linear damping and additive noise. Since no Poincaré inequality is available on the whole plane, the damping term is crucial for obtaining uniform-in-time estimates. I will discuss the existence of invariant measures and then focus on uniqueness. The main result shows that, if the damping coefficient is sufficiently large compared with the noise intensity, then the associated Markov semigroup admits a unique invariant probability measure. The proof is based on anisotropic energy estimates, exponential martingale estimates, and an asymptotic coupling argument. The result applies to general additive noise and requires no non-degeneracy condition.

报告人简介：梁思玉，博士毕业于中国科学院大学和德国比勒菲尔德大学，现为南京理工大学数学与统计学院讲师，主要从事随机偏微分方程，特别是流体力学相关方程的理论研究。相关工作发表于 J. Differential Equations、J. Math. Anal. Appl.、Z. Angew. Math. Phys. 等期刊。