Events
Department of Mathematics and Statistics
Texas Tech University
In this talk, we will investigate the propagation of Lipschitz regularity by solutions to various nonlinear, nonlocal parabolic equations. We will locally analyze models such as the Michelson-Sivashinsky equation, incompressible Navier-Stokes system, and advection diffusion problems that include the dissipative SQG equation. Depending on the model, we will either show global well-posedness, derive new regularity criteria, or provide different proofs to and generalize previously obtained results. In particular, and if time allows, we will show that for abstract drift-diffusion problems, it is possible to break certain, supercritical Holder-type barriers and get regularity, which is rather surprising.
To join the talk on Zoom please click
here.
We approach manifold topology by examining configurations of finite subsets of manifolds within the homotopy-theoretic context of $\infty$-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration spaces in the case of Euclidean space in terms of the category $\Theta_n$.  | Wednesday
Feb. 2
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| Algebra and Number Theory
No Seminar
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The BGK model was introduced by Bhatnagar, Gross and Krook as a relaxation model for the fundamental Boltzmann equation, which describes the kinetic dynamic of rarefied gases with a probability distribution function. We propose an efficient, high order accurate and asymptotic-preserving (AP) semi-Lagrangian (SL) method for the BGK model with constant or spatially dependent Knudsen number. Our numerical scheme is composed of a mass conservative SL nodal discontinuous Galerkin (NDG) method as spatial discretization; together with third order AP and asymptotically accurate (AA) diagonally implicit Runge-Kutta (DIRK) methods for the stiff relaxation term along characteristics. The AA time discretization methods are constructed based on an accuracy analysis of the SL scheme for stiff hyperbolic relaxation systems and kinetic BGK model in the limiting fluid regime when the Knudsen number approaches 0. An extra order condition for the asymptotic third order accuracy in the limiting regime is derived. Linear von Neumann stability analysis of the proposed third order DIRK methods are performed to a simplified two-velocity linear kinetic model. Extensive numerical tests are presented to demonstrate the AA, AP and stability properties of our proposed schemes
Please virtually attend the Applied Math seminar via this Zoom link Wednesday the 2nd at 4 PM -- meeting ID: 937 2431 1192