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SUMMARY:Dallas Albritton (Courant Institute\, New York)
DTSTART:20201019T160000Z
DTEND:20201019T165000Z
DTSTAMP:20260423T024752Z
UID:anpdews/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/38/"
 >Self-similar solutions of active scalars with critical dissipation</a>\nb
 y Dallas Albritton (Courant Institute\, New York) as part of HA-GMT-PDE Se
 minar\n\n\nAbstract\nIn PDE analyses of fluid models\, often we may identi
 fy a so-called critical space that lives precisely at the borderline betwe
 en well-posedness and ill-posedness. What happens at this borderline? We e
 xplore this question in two active scalar equations with critical dissipat
 ion. In the surface quasi-geostrophic equations\, we investigate the conne
 ction between non-uniqueness and large self-similar solutions that was est
 ablished by Jia\, Sverak\, and Guillod in the Navier-Stokes equations. Thi
 s is joint work with Zachary Bradshaw. In the critical Burgers equation\, 
 and more generally in scalar conservation laws\, the analogous self-simila
 r solutions are unique\, and we show that all front-like solutions converg
 e to a self-similar solution at the diffusive rates. This is joint work wi
 th Raj Beekie.\n
LOCATION:https://researchseminars.org/talk/anpdews/38/
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