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Home » Graduate Student Working Group: Uniform Lifetime of Classical Solutions of the Hot, Magnetized Relativistic Vlasov Maxwell System & Equivalence of function space and pure Banach space properties

Seminar

Graduate Student Working Group: Uniform Lifetime of Classical Solutions of the Hot, Magnetized Relativistic Vlasov Maxwell System & Equivalence of function space and pure Banach space properties March 10, 2021 (11:10 AM PST - 12:10 PM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Dayton Preissl (University of Victoria), Mitchell Taylor (University of California, Berkeley)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

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Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

11:10 Speaker: Dayton Preissl (University of Victoria)



Title: Uniform Lifetime of Classical Solutions of the Hot, Magnetized Relativistic Vlasov Maxwell System



Abstract: This talk describes the well posedness of the Hot, Magnetized, Relativistic Vlasov Maxwell System (HMRVM) which models magnetized plasma, such as fusion devices. In the absence of an external magnetic field, the Relativistic, Vlasov Maxwell system (RVM) is well understood. The RVM system admits global C^1 solutions for small, decaying data and local solutions for large data. Global solutions for large data remains an open problem. In this talk I explain a very recent result of a sufficient condition on the initial data and physical constraints on the large external field which imply some type of linear stability of C^1 solutions with uniform sup-norm control to the HMRVM system. I further discuss the proof of a uniform lower bound on the lifetime of classical solutions for arbitrarily large external fields and demonstrate the novel techniques with a simple toy model.





​11:40 Speaker: Mitchell Taylor (University of California, Berkeley)



Title: Equivalence of function space and pure Banach space properties



Abstract: This is, in some sense, an extension of the Ribe program, which was initiated by Bourgain and Lindenstrauss in 1985, and is currently led by Naor. Of course, my talk will be very introductory, and won't get too far into the state of the art.

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