
Date Time 
Location  Speaker 
Title – click for abstract 

09/26 3:00pm 
BLOC 302 
William M Golding University of Texas at Austin 
Strong solutions for the homogeneous Landau equation
The Landau equation is one of the fundamental models of statistical physics for describing the evolution of plasmas. Nevertheless, the existence of globalintime smooth solutions remains widely open, even for the homogeneous equation. I will discuss some recent progress in constructing localintime strong solutions for large initial data under minimal integrability assumptions. Our method relies crucially on a priori short time smoothing estimates obtained via the De Giorgi method. While for Landau these smoothing estimates require some integrability assumptions on the initial data, these assumptions may be removed for critical perturbations of the Landau equation. Consequently, arbitrarily small critical perturbations of the Landau equation admit globalintime smooth solutions for generic, possibly large initial data. 

10/10 3:00pm 
Zoom 
Lucas Huysmans University of Cambridge 
Nonuniqueness and inadmissibility of the vanishing viscosity limit of the passive scalar transport equation
We study the vanishing viscosity/diffusivity limit of the passive scalar transport equation along a given bounded divergencefree vector field on
the twodimensional torus. We construct two such velocity vector fields each
exhibiting peculiar behaviour. For the first we demonstrate that along different subsequences of viscosities the limit of transport may converge strongly to different solutions to the inviscid transport. Both of these limits are renormalised solutions to the transport equation, and so equally physically admissible. For the second velocity vector field we prove the uniqueness of the vanishing viscosity limit of viscous transport, however, for any initial data, this unique vanishing viscosity solution is mixed to its spatial average and after a short delay perfectly unmixes to its original state. Therefore the vanishing viscosity limit exhibits a dissipation of energy/entropy and later a reverse of this
dissipation. 

10/17 3:00pm 
Zoom/See link be 
Hussain Ibdah University of Maryland 
Bypassing Holder supercriticality barriers in viscous, incompressible fluids
We will go over the main ideas used in showing that as long as supercritical Holder seminorms of the classical solution to the incompressible NavierStokes system (in any dimension) are under control, the solution remains smooth. The key idea is exploiting an enhanced regularity effect coming from the transport term at the level of a simple onedimensional driftdiffusion equation, allowing us to break the criticality barrier. We then employ ideas introduced by Kiselev, Nazarov, Volberg, and Shterenberg to propagate this to abstract driftdiffusion equations, providing to our knowledge the very first reasonable extension of the celebrated parabolic regularity result of Nash to an equation that is not in divergence form. Such an approach coupled with subtle pressure estimates due to Silvestre allows us to rigorously treat the incompressible NavierStokes as a perturbation of driftdiffusion, obtaining, to our knowledge, the very first genuinely supercritical regularity criterion for this system of equations.
Zoom link: https://tamu.zoom.us/j/93413906718?pwd=VDlXYS8zbm9uQ2dMWGowcGVOeGRPdz09


10/24 3:00pm 
BLOC 302 
Collin Victor Texas A&M University 
Leveraging Observational Data to Enhance Continuous Data Assimilation
In this talk, I will discuss my investigation of a computationally efficient algorithm for data assimilation in recovering solutions to turbulent fluids, specifically the AzouaniOlsonTiti continuous data assimilation algorithm. I will present modifications aimed at enhancing the algorithm's performance while maintaining its relevance to physically realistic use cases. Furthermore, I will demonstrate the application of the algorithm to a range of dissipative partial differential equations, from the 1D AllenCahn equation to the 2D and 3D NavierStokes equations, and a highresolution realistic ocean model. A key focus of my research is the role of observational data in convergence rates, examining optimal strategies for gathering observations, and effectively assimilating sparse observational data. Through my analysis, I provide insights into improving turbulent fluid recovery by leveraging the algorithm's potential in various scenarios and identifying the crucial factors that contribute to its success. 

10/31 3:00pm 
BLOC 302 
Yongming Li Texas A&M University 
Dispersive estimates for 1D matrix Schrödinger operators with threshold resonance
In this talk, we will discuss dispersive and local decay
estimates for a class of matrix Schrödinger operators that naturally
arise from the linearization of focusing nonlinear Schrödinger equations
around a solitary wave. We review the spectral properties of these
linearized operators, and discuss how threshold resonances may appear in
their spectrum. In the presence of threshold resonances, it will be
shown that the slowdown of the local decay rate can be pinned down to
a finite rank operator corresponding to the threshold resonances. Some
applications for the linearized equation for the 1D focusing cubic
Schrödinger equation will be discussed. 

12/05 3:00pm 
BLOC 302 
Maxime van de Mortel Rutgers University 
Asymptotic behavior of the KleinGordon equation on a Schwarzschild black hole
It has long been conjectured that the KleinGordon equation on a Schwarzschild black hole behaves very differently from the wave equation at latetimes, and only decays at a slow t^{5/6} rate. Despite its apparent simplicity, this conjecture had remained open. We discuss its resolution and our recent result establishing latetime tails at the rate t^{5/6} for each angular mode.
Joint work with Federico Pasqualotto and Yakov ShlapentokhRothman.
