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X-WR-CALDESC:FAU DCN-AvH. Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship
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DTSTART;TZID=Europe/Berlin:20221130T173000
DTEND;TZID=Europe/Berlin:20221130T183000
DTSTAMP:20221021T095911Z
CREATED:20221021
LAST-MODIFIED:20221130
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SUMMARY:Compensated Integrability and Conservation Laws
DESCRIPTION:Next Wednesday, November 30, 2022:\nEvent: FAU DCN-AvH Seminar\nOrganized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)\nTitle: Compensated Integrability and Conservation Laws\nSpeaker: Prof. Dr. Denis Serre\nAffiliation: Ecole Normale Supérieure de Lyon (France).\nAbstract. Compensated Integrability is a recent tool from Functional Analysis. It applies to positive semi-definite tensors whose row-wise Divergence is a finite measure. Quite often, this Divergence vanishes identically. We shall explain why Div-free tensors occur naturally in various models of Mathematical Physics, as a consequence of N{\oe}ther’s Theorem. \nSomehow, Compensated Integrability is dual to Brenier’s existence result for the “second BVP” for the Monge-Ampère equation. It extends in a non-trivial manner classical statements, such as Gagliardo-Nirenberg-Sobolev Inequality, or the Isoperimetric Inequality. In the periodic situation, it expresses the Div-quasiconcavity of A\mapsto(\det A)^{\frac1{n-1}} (recall that A\mapsto(\det A)^{\frac1n} is concave over {\bf Sym}_n^+). This leads to a weak upper-semicontinuity result (collaboration with L. De Rosa & R. Tione).\nWhen it applies, C.I. yields dispersive (Strichartz-like) estimates. We thus learn that in Gas Dynamics, the internal energy cannot concentrate on zero-measure subsets. Other applications concern various models for particle dynamics: kinetic equations (Boltzman), mean-field models (Vlasov), molecular dynamics. The corresponding tensor is positive semi-definite whenever the particles interact pairwise according to a radial, repulsive force. Hard spheres dynamics shows that a Div-free tensor can be supported by a small set (here a graph), in which case a special form of C.I. is required.\nAnother relevant topic is that of multi-dimensional conservation laws, where it allows us to extend Kruzkov’s theory to L^p-data when p is finite, under a non-degeneracy assumption (collaboration with L. Silvestre).\nWHERE?\nOn-site / online\nOn-site:\nRoom 12801.01.252 (Übung 3 / 01.252-128) \n1st floor of the Felix Klein building (Dep. Mathematik)\nFriedrich-Alexander-Universität Erlangen-Nürnberg\nCauerstraße 11, 91058 Erlangen\nGPS-Koord. Raum: 49.573701N, 11.030613E\nOnline:\nZoom meeting link\nMeeting ID: 614 4658 159 | PIN code: 914397\n\n
URL:https://dcn.nat.fau.eu/events/compensated-integrability-and-conservation-laws/
ORGANIZER;CN=FAU DCN-AvH:MAILTO:
CATEGORIES:FAU DCN-AvH Seminar,Seminar/Talk
LOCATION:DDS, Friedrich-Alexander-Universität Erlangen-Nürnberg
ATTACH;FMTTYPE=image/png:https://dcn.nat.fau.eu/wp-content/uploads/FAUDCNAvH-seminar-30nov2022-dSerre.png
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