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SUMMARY:Nonunique solutions of the transport equation for Sobolev vector f
 ields
DTSTART:20240322T141500
DTSTAMP:20260428T115500Z
UID:9408baf289a98ebe44f7cc70e97104f881ac808e7601c4a87ca64fe8
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Anuj Kumar (Berkeley)\nAbstract: This talk is based on 
 recent work jointly with E. Bruè and M. Colombo. We construct nonunique\n
 solutions of the continuity equation in the class L^\\infty in time and L^
 r\nin space. We achieve this by introducing two novel ideas: (1) In the co
 nstruction\, we interweave the scaled copies of\nthe vector field itself. 
 (2) Asynchronous translation of cubes\, which makes the construction\nhete
 rogeneous in space. These new ideas allow us to prove nonuniqueness in the
  range of\nexponents beyond what is available using the method of convex i
 ntegration and sharply match\nwith the range of uniqueness of solutions fr
 om Bruè\, Colombo\, De Lellis ’21.
LOCATION:MA B1 11 https://plan.epfl.ch/?room==MA%20B1%2011
STATUS:CONFIRMED
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