BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20190331T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20191027T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190514T093000
DTEND;TZID=Europe/Paris:20190514T120000
DTSTAMP:20260410T015936
CREATED:20190514T073000Z
LAST-MODIFIED:20211025T103550Z
UID:8493-1557826200-1557835200@www.math.ens.psl.eu
SUMMARY:Nonuniqueness for the Navier–Stokes equations and model equations / Singularities in Fluid Mechanics
DESCRIPTION:JG: In this talk\, I will discuss fundamental properties of the solutions to the incompressible Navier–Stokes equations in three dimensions. After reviewing the classical local well-posedness results\, I will explain how numerical simulations suggest local ill-posedness at the borderline of the known results. I will discuss a plausible scenario of non-uniqueness from smooth initial data through finite-time blow-up. Finally\, I will describe how this scenario is actually happening in a model equation sharing the same fundamental properties as the Navier–Stokes equations.KM: Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or\, in an evolving flow\, becomes infinite at any point within a finite time). Such singularities can be mathematical but unphysical (as e.g. in two-dimensional flow near a sharp corner) in which case they can be ‘resolved’ by improving the physical model considered; or they can be physical but non-mathematical (as e.g. in the case of cusp singularities at a fluid/fluid interface) in which case resolution of the singularity may involve incorporation of additional physical effects; these examples will be briefly reviewed. The `finite-time singularity problem’ for the Navier-Stokes equations will then be discussed and a new analytical approach will be presented; here it will be shown that there is indeed a singularity of the ‘physical but non-mathematical’ type\, in that\, at suf- ficiently high Reynolds number\, vorticity can be amplified by an arbitrarily large factor within a finite time. In this case\, the singularity is resolved by three-dimensional vortex re- connection in a manner that admits analytical description.
URL:https://www.math.ens.psl.eu/evenement/nonuniqueness-for-the-navier-stokes-equations-and-model-equations-singularities-in-fluid-mechanics/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Analyse non linéaire et EDP
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190514T140000
DTEND;TZID=Europe/Paris:20190514T170000
DTSTAMP:20260410T015936
CREATED:20190514T120000Z
LAST-MODIFIED:20211104T135214Z
UID:8510-1557842400-1557853200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Stefan Witzel (Ecole Polytehchnique)15.00-15.45 Katie Vokes (IHES)15.45-16.15 coffee break16.15-16.45 Adrien Le Boudec (ENS Lyon)Stefan Witzel\, Arithmetic approximate groups and their finiteness propertiesI will talk about approximate groups\, a geometric generalization of groups. Approximate groups were discovered independently in various contexts and I will describe how they arise very naturally in the context of arithmetic groups. I will then explain how to extend topological finiteness properties of groups to approximate groups. This allows to make a connection betweenarithmetic groups in positive characteristic and arithmetic approximate groups in characteristic zero. The talk is based on joint work with Tobias Hartnick.Katie Vokes\, Hierarchical hyperbolicity of graphs associated to surfacesIn a paper of 2000\, Masur and Minsky studied the geometry of mapping class groups of surfaces using projections to certain Gromov hyperbolic graphs (the curve graphs) associated to subsurfaces. This inspired the definition by Behrstock\, Hagen and Sisto of hierarchically hyperbolic spaces\, which are equipped with similar projection maps\, satisfying conditions which guarantee a structure analogous to that of the mapping class group. I will give some background on these concepts and present a result demonstrating that a large family of graphs associated to surfaces are hierarchically hyperbolic spaces.Adrien Le Boudec\, Simple groups having a wreath product as a geometric modelThe goal of the talk will be to describe groups that are finitelygenerated\, simple\, and that act properly and cocompactly on thenatural Cayley graph of the wreath product A wr F\, where A is afinite group and F a non-abelian free group.
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-3/
LOCATION:Salle W (DMA)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
END:VCALENDAR