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UID:news1713@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20241112T142345
DTSTART;TZID=Europe/Zurich:20241120T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Tommaso Cortopassi (Scuo
 la Normale Superiore di Pisa)
DESCRIPTION:We introduce a new stability estimate for comparing the regular
  Lagrangian flow of a Sobolev vector field to a piecewise affine approxima
 tion generated by an explicit Euler-like method\, in the spirit of Crippa-
 De Lellis's estimates. We use this estimate to prove approximation results
  for solutions of the continuity equation\, which can be represented as th
 e push forward of the initial datum via the regular Lagrangian flow. We gi
 ve two examples: a probabilistic one using Dirac deltas to approximate the
  initial datum and a deterministic one using a diffuse approximation inste
 ad. In both cases\, we assume no regularity on the mesh partitioning the s
 patial domain.
X-ALT-DESC:<p>We introduce a new stability estimate for comparing the regul
 ar Lagrangian flow of a Sobolev vector field to a piecewise affine approxi
 mation generated by an explicit Euler-like method\, in the spirit of Cripp
 a-De Lellis's estimates. We use this estimate to prove approximation resul
 ts for solutions of the continuity equation\, which can be represented as 
 the push forward of the initial datum via the regular Lagrangian flow. We 
 give two examples: a probabilistic one using Dirac deltas to approximate t
 he initial datum and a deterministic one using a diffuse approximation ins
 tead. In both cases\, we assume no regularity on the mesh partitioning the
  spatial domain.</p>
DTEND;TZID=Europe/Zurich:20241120T160000
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