Fluids Mechanics and Waves Seminar - Spring 2025 | Department of Mathematical Sciences

For questions about the seminar schedule, please contact Thi Phong Nguyen.

February 27

Jiajie Chen, Courant Institute, New York University

Singularity Formation in Fluids

Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is a long-standing open problem in mathematical fluid mechanics. In this talk, I will begin by providing an overview of this problem and then introduce a framework for stable, nearly self-similar blowup, developed in joint work with Tom Hou (Caltech). Using this framework, we establish singularity formation in the incompressible Euler equations with smooth data and boundary. Additionally, I will briefly present recent results on vorticity blowup in compressible Euler equations and beyond, using the self-similar blowup method.

Homepage: https://jiajiechen94.github.io/

March 10

Svetlana Tlupova, Farmingdale State College, State University of New York

Regularization based methods for evaluating single and double layer surface integrals in Stokes flow

We will give an overview of joint work with J. Thomas Beale on numerical methods for computing the single and double layer integrals on closed surfaces in Stokes flow. The Stokeslet and stresslet kernels are singular when evaluated on the surface and nearly singular when evaluated near the surface, which is the most difficult case to compute accurately. The kernels are first regularized, or smoothed out, using a length scale parameter. In one approach, corrections for the smoothing error are derived analytically using local analysis and added to obtain about third order accuracy. As an alternative approach, an extrapolation strategy is to compute the regularized integral for three choices of the smoothing parameter and solve for the extrapolated value of the integral with about fifth order accuracy. When evaluating the integrals on the surface, as needed when solving integral equations, special smoothing can be used so that high accuracy is obtained without needing corrections or extrapolation.

Homepage: https://www.farmingdale.edu/faculty/?fid=52171