Applied Mathematics and Analysis Seminar

As part of the Duke University Department of Mathematics, the Program in Applied Mathematics hosts this ongoing series of seminars. The presentations cover a broad range of topics including numerical analysis, ordinary and partial differential equations, nonlinear systems, scientific computing, dynamical systems theory, mathematical biology, pattern formation, and complex physical systems.

To join the applied mathematics mailing list visit: subscribe applied-math-seminar

As a convenience, some selected seminars and presentations can be viewed live via the web. Further, we have video archives of past talks, which are also publicly available for you to view at any time.

Upcoming Seminars:

Tuesday, April 16, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
Absence of anomalous dissipation in the 2D Navier Stokes equations
Jaemin Park (University of Basel)

In this talk, we will discuss Leray-Hopf solutions to the two-dimensional Navier-Stokes equations with vanishing viscosity. We aim to demonstrate that when the initial vorticity is only integrable, the Leray-Hopf solutions in the vanishing viscosity limit do not exhibit anomalous dissipation. Moreover, we extend this result to the case where the initial vorticity is merely a Radon measure, assuming its singular part maintains a fixed sign. Our proof draws on several key observations from the work of J. Delort (1991) on constructing global weak solutions to the Euler equation. This is a joint work with Luigi De Rosa (University of Basel).
Tuesday, April 23, 2024, 3:15pm, Physics 119, Applied Math And Analysis Seminar
Small scale creation of the Lagrangian flow in 2d perfect fluids
Ayman Said (University of Cambridge)

In this talk I will present a recent result showing that for all solutions of the 2d Euler equations with initial vorticity with finite Sobolev smoothness then an initial data dependent norm of the associated Lagrangian flow blows up in infinite time like $t^{\frac{1}{3}}$. This initial data dependent norm quantifies the exact $L^2$ decay of the Fourier transform of the solution. This adapted norm turns out to be the exact quantity that controls a low to high frequency cascade which I will then show to be the quantitative phenomenon behind a microlocal generalized Lyapunov function constructed by Shnirelman.

All seminars take place on Mondays at 4:30 pm in Room 119 Physics Building unless otherwise noted.