Quyuan Lin

Quyuan Lin is an Assistant Professor in the School of Mathematical and Statistical Sciences at Clemson University. He previously served as a Visiting Assistant Professor in the Department of Mathematics at UC Santa Barbara (2021–2023) and earned his Ph.D. from Texas A&M University under Dr. Edriss Titi. His research focuses on nonlinear partial differential equations (PDEs) in fluid dynamics, particularly geophysical and electrohydrodynamic contexts. Lin's work addresses theoretical and applied challenges in fluid mechanics, stochastic systems, and mathematical analysis of PDEs.

Education:

• Ph.D., Texas A&M University, 2021

Research Interests: Lin investigates nonlinear PDEs arising in geophysical fluid dynamics, such as primitive equations and Navier-Stokes systems, with applications to electrohydrodynamics and stochastic processes. His studies emphasize well-posedness, singularity formation, and numerical approximation using methods like physics-informed neural networks. Key areas include fluid-structure interactions, anisotropic viscosities, and ergodic properties of stochastic fluid models.

Publications Trends: Recent work explores stochastic regularization in inviscid systems, coarsening dynamics in phase separation models, and the interplay between transport noise and well-posedness in Boussinesq and Nernst-Planck systems. Lin also analyzes long-time behavior and ergodicity in coupled stochastic PDEs, contributing to both theoretical foundations and computational methods.

Affiliations & Activities: Lin leads the Clemson Analysis & PDE Seminar and maintains an active research group focused on fluid dynamics and stochastic PDEs. His work bridges pure analysis and applied mathematics, with implications for climate modeling and material science.