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SUMMARY:Matthew Rosenzweig (MIT)
DTSTART:20211028T130000Z
DTEND:20211028T135000Z
DTSTAMP:20260423T052549Z
UID:IMS/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/82/">Glo
 bal solutions of aggregation equations and other flows with random diffusi
 on</a>\nby Matthew Rosenzweig (MIT) as part of PDE seminar via Zoom\n\n\nA
 bstract\nAggregation equations\, such as the parabolic-elliptic Patlak-Kel
 ler-Segel model\, are known to have an optimal threshold for global existe
 nce vs. finite-time blow-up. In particular\, if the diffusion is absent\, 
 then all smooth solutions with finite second moment can exist only locally
  in time. Nevertheless\, one can ask whether global existence can be resto
 red by adding a suitable noise to the equation\, so that the dynamics are 
 now stochastic. In this talk\, we investigate whether random diffusion can
  restore global existence for a large class of active scalar equations in 
 arbitrary dimension with possibly singular velocity fields. This class inc
 ludes Hamiltonian flows\, such as the SQG equation and its generalizations
 \, and gradient flows\, such as those arising in aggregation models. For t
 his class\, we show global existence of solutions in Gevrey-type Fourier-L
 ebesgue spaces with quantifiable high probability.\n
LOCATION:https://researchseminars.org/talk/IMS/82/
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