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SUMMARY:Geometric interpretation of the vanishing Lie Bracket for two-dime
 nsional rough vector fields - Annalaura Rebucci\, MPI Leipzig
DTSTART:20250526T130000Z
DTEND:20250526T140000Z
UID:TALK231877@talks.cam.ac.uk
CONTACT:Amelie Justine Loher
DESCRIPTION:A classical result in differential geometry\, ultimately lead
 ing to Frobenius theorem\, states that the flows of two smooth vector fiel
 ds X\, Y commute for all times if and only if their Lie bracket [X\,Y] van
 ishes. In this talk\, we consider continuous\, Sobolev vector fields with 
 bounded divergence on the real plan\, and we discuss an extension of the c
 lassical Frobenius theorem in the setting of Regular Lagrangian Flows. In 
 particular\, we improve the previous result of Colombo-Tione (2021)\, wher
 e the authors require the additional assumption of the weak Lie different
 iability on one of the two flows. This is a joint project in collaboration
  with Martina Zizza.
LOCATION:MR13
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