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BEGIN:VEVENT
UID:2024110503382020241104T16000020241104T165000672a3becd8fe4@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20241104T042735
DTSTART:20241104T160000
DTEND:20241104T165000
SUMMARY:Analysis and Applied Mathematics Seminar: Recent progress on global solutions to the homogeneous Landau equation, by William Golding
DESCRIPTION:William Golding (University of Chicago): Recent progress on global solutions to the homogeneous Landau equation The Landau equation in kinetic theory is one of the fundamental kinetic equations that describes the evolution of collisional plasmas. The equation includes a quadratic, non-local term that models the effects of binary collisions mediated by the Coulomb force. This collision term introduces substantial mathematical challenges, leaving many fundamental questions--such as the existence of global-in-time smooth solutions--largely open. In this talk, I will explore recent progress made in understanding a simplified model, the homogeneous Landau equation, which retains the complex collision term. In a recent breakthrough work, Luis Silvestre and Nestor Guillen showed the existence of a new monotone functional---the Fisher information---which is used to construct global-in-time solutions for smooth rapidly decaying initial data. I will discuss joint work with Maria Gualdani and Amelie Loher, where we extend these results to general initial data and obtain new results on global-in-time existence and various forms of uniqueness. I will conclude with a discussion of how these results inform future research of the full model. Please click here to make changes to, or delete, this seminar announcement. | Event post: https://mscs.uic.edu/events?page_id=5191117
LOCATION:636 SEO Chicago IL
CLASS:PRIVATE
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