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UID:news1638@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20240328T104112
DTSTART;TZID=Europe/Zurich:20240417T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Anuj Kumar (UC Berkeley)
DESCRIPTION:We construct nonunique solutions of the transport equation in t
 he class $L^\\infty$ in time and $L^r$ in space for divergence free Sobole
 v vector fields $W^{1\, p}$. We achieve this by introducing two novel idea
 s: (1) In the construction\, we interweave the scaled copies of the vector
  field itself. (2) Asynchronous translation of cubes\, which makes the con
 struction heterogeneous in space. These new ideas allow us to prove nonuni
 queness in the range of exponents beyond what is available using the metho
 d of convex integration and sharply matchwith the range of uniqueness of s
 olutions from Bruè\, Colombo\, De Lellis ’21. 
X-ALT-DESC:<p>We construct nonunique solutions of the transport equation in
  the class $L^\\infty$ in time and $L^r$ in space for divergence free Sobo
 lev vector fields $W^{1\, p}$. We achieve this by introducing two novel id
 eas: (1) In the construction\, we interweave the scaled copies of the vect
 or field itself. (2) Asynchronous translation of cubes\, which makes the c
 onstruction heterogeneous in space. These new ideas allow us to prove nonu
 niqueness in the range of exponents beyond what is available using the met
 hod of convex integration and sharply matchwith the range of uniqueness of
  solutions from Bruè\, Colombo\, De Lellis ’21.&nbsp\;</p>
DTEND;TZID=Europe/Zurich:20240417T160000
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