Current Appointments & Affiliations
Professor of Mathematics
·
2024 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Regular and Singular Steady States of the 2D Incompressible Euler Equations near the Bahouri–Chemin Patch
Journal Article Archive for Rational Mechanics and Analysis · February 1, 2025 We consider steady states of the two-dimensional incompressible Euler equations on T2 and construct smooth and singular steady states around a particular singular steady state. More precisely, we construct families of smooth and singular steady solutions t ... Full text CiteNorm Growth, Non-uniqueness, and Anomalous Dissipation in Passive Scalars
Journal Article Archive for Rational Mechanics and Analysis · December 1, 2024 We construct a divergence-free velocity field u:[0,T]×T2→R2 satisfying (Formula presented.) such that the corresponding drift-diffusion equation exhibits anomalous dissipation for all smooth initial data. We also show that, given any α0<1, the flow can be ... Full text CiteTwisting in Hamiltonian flows and perfect fluids
Journal Article Inventiones Mathematicae · October 1, 2024 We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to establish a number ... Full text CiteRecent Grants
CAREER:Formation of Small Scales and Dissipation in Incompressible Fluids
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2025Sloan Foundation Fellowship for Tarek Elgindi in Mathematics
FellowshipPrincipal Investigator · Awarded by Alfred P. Sloan Foundation · 2020 - 2024Singularity Formation in Incompressible Fluids
ResearchPrincipal Investigator · Awarded by Simons Foundation · 2023 - 2024View All Grants
Education, Training & Certifications
New York University ·
2014
Ph.D.