Overview
My current research interests focus on mathematical fluid mechanics and mathematical biology.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators.
Current Appointments & Affiliations
William T. Laprade Distinguished Professor of Mathematics
·
2018 - Present
Mathematics,
Trinity College of Arts & Sciences
Professor of Mathematics
·
2017 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Finite time blow-up in a 1D model of the incompressible porous media equation
Journal Article Nonlinearity · May 31, 2025 We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdo ... Full text CiteThe α-SQG patch problem is illposed in C2,β and W2,p
Journal Article Communications on Pure and Applied Mathematics · April 1, 2025 We consider the patch problem for the (Formula presented.) -(surface quasi-geostrophic) SQG system with the values (Formula presented.) and (Formula presented.) being the 2D Euler and the SQG equations respectively. It is well-known that the Euler patches ... Full text Open Access CiteSuppression of chemotactic blowup by strong buoyancy in Stokes-Boussinesq flow with cold boundary
Journal Article Journal of Functional Analysis · October 1, 2024 In this paper, we show that the Keller-Segel equation equipped with zero Dirichlet Boundary condition and actively coupled to a Stokes-Boussinesq flow is globally well-posed provided that the coupling is sufficiently large. We will in fact show that the dy ... Full text Open Access CiteRecent Grants
Small Scale and Singularity Formation in Fluids
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2026RTG: Training Tomorrow's Workforce in Analysis and Applications
Inst. Training Prgm or CMEPrincipal Investigator · Awarded by National Science Foundation · 2021 - 2026Small Scale and Singularity Formation in Fluids
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2025View All Grants
Education, Training & Certifications
California Institute of Technology ·
1997
Ph.D.