报告人：牟丽颖 博士
报告题目：Well-posedness and Quantitative Stability for Degenerate Fokker–Planck Equations with Rough Coefficients
报告时间：2026年10月11日（周日）上午9：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
牟丽颖，天津大学在读博士生（四年级），师从王凤雨教授，已在Rev. Mat. Complut.等杂志上发表论文。
报告摘要：
We establish quantitative stability and well-posedness for degenerate Fokker–Planck equations with Sobolev-regular and possibly fully degenerate diffusion coefficient. For two classes of rough drifts, stability estimates imply uniqueness, and existence is proved under suitable conditions. First, for anisotropic drifts with partial fractional Sobolev regularity, we prove both existence (as probability densities, essential for the probabilistic interpretation via superposition) and quantitative stability without imposing any growth conditions, covering the full range of fractional exponents and extending previous Lagrangian-flow results. Second, for drifts whose distributional gradients are given by singular integrals (e.g., Biot–Savart velocity fields from L^1 vorticity), we obtain stability estimates that allow the diffusion matrix to be time-space dependent and possibly degenerate, removing the prior restrictions of identity diffusion or bounded coefficients. Our results also recover the pure transport regime as a limiting case.