Organizers: Albert Kunhui Luan (kunhui.luan@sc.edu), Qiyu Wu (QIYU@email.sc.edu), Jesse Singh (jasdeep@email.sc.edu), Haonan Zhang (haonanz@mailbox.sc.edu)

This is a student-led seminar that focuses on applications of harmonic analysis to PDEs and mathematical fluid dynamics, including the analysis of singular integrals of the Calderon–Zygmund type, fractional Laplacians, various interpolation results, and Littlewood–Paley localization. The discussion will be based on selected papers and references listed below.

Papers

1. Blow-up and regularity for the fractal Burgers equation
2. The fractional p-Laplacian evolution equation in ℝ^N in the sublinear case

Literature References

1. The Mathematical Analysis of the Incompressible Euler and Navier–Stokes Equations
2. Classical and Multilinear Harmonic Analysis, Vol. 1
3. Hitchhikerʼs Guide to the Fractional Sobolev Spaces

Meeting Time & Location: Every Wednesday, 10:30 a.m. – 11:30 a.m., LC 346

Everyone is welcome to join! There are plenty of opportunities to read parts of the papers and present results.

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2025 - 2026 Academic Year

Expand all9/10 -  Viscous and inviscid Burgers equation; regularity vs. blow-up, Cole–Hopf transformation, and introduction to fractional Laplacian operator.

Date: September 10, 2025

Topic: Viscous and inviscid Burgers equation; regularity vs. blow-up, Cole–Hopf transformation, and introduction to fractional Laplacian operator.