Items filtered by date: Thursday, 19 October 2023
Primitive equations: mathematical analysis and machine learning algorithm
Speaker: Quyuan Lin (Clemson University)
Large scale dynamics of the ocean and the atmosphere are governed by the primitive equations (PE). In this presentation, I will first review the derivation of the PE and some well-known results for this model, including well-posedness of the viscous PE and ill-posedness of the inviscid PE. The focus will then shift to discussing singularity formation and the stability of singularities for the inviscid PE, as well as the effect of fast rotation (Coriolis force) on the lifespan of the analytic solutions. Finally, I will talk about a machine learning algorithm, the physics-informed neural networks (PINNs), for solving the viscous PE, and its rigorous error estimate.
Time: November 17, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Changhui Tan
Sticky particles with sticky boundary: well-posedness and asymptotic behavior
Speaker: Adrian Tudorascu (West Virginia University)
We study Zeldovich's Sticky-Particles system when the evolution is confined to arbitrary closed subsets of the real line. Only the sticky boundary condition leads to a rigorous formulation of the initial value problem, whose well-posedness is proved under the Oleinik and initial strong continuity of energy conditions. For solutions confined to compact sets a long-time asymptotic limit is shown to exist.
Time: October 27, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Changhui Tan