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BEGIN:VEVENT
UID:dc7a86e1f544cfd1700c29c4cab39c20
CATEGORIES:Nonlinear Analysis
CREATED:20210125T092542
SUMMARY:Flows of vector fields: classical and modern
LOCATION:Zoom
DESCRIPTION:<p><strong>Abstract:&nbsp;</strong>Consider a (possibly time-dependent) vec
 tor field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (also 
 named Picard-Lindel"of) Theorem states that, if the vector field $v$ is Lip
 schitz in space, for every initial datum $x$ there is a unique trajectory $
 gamma$ starting at $x$ at time $0$ and solving the ODE $dot{gamma} (t) = v 
 (t, gamma (t))$. The theorem looses its validity as soon as $v$ is slightly
  less regular. However, if we bundle all trajectories into a global map all
 owing $x$ to vary, a celebrated theory put forward by DiPerna and Lions in 
 the 80es show that there is a unique such flow under very reasonable condit
 ions and for much less regular vector fields. A long-standing open question
  is whether this theory is the byproduct of a stronger classical result whi
 ch ensures the uniqueness of trajectories for {em almost every} initial dat
 um. I will give a complete answer to the latter question and draw connectio
 ns with partial differential equations, harmonic analysis, probability theo
 ry and Gromov's $h$-principle.&nbsp;</p>
CONTACT:Camillo De Lellis, Institute for Advanced Study
X-EXTRAINFO:https://rutgers.zoom.us/j/94175715705?pwd=NEh2ak9nVzlmczZ6a1RMY0VBUFlEQT09#
 succe\n Meeting ID: 941 7571 5705   Passcode: 849396\n
DTSTAMP:20260828T183830
DTSTART;TZID=America/New_York:20210203T093000
DTEND;TZID=America/New_York:20210203T103000
SEQUENCE:0
TRANSP:OPAQUE
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