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UID:b6a580da0c7a116cf68e002d4f000058
CATEGORIES:Colloquia
CREATED:20250210T134645
SUMMARY:On Hilbert’s sixth problem
LOCATION:HILL 705
DESCRIPTION:Hilbert’s sixth problem asks for the axiomatic derivation of the laws of ph
 ysics from first principles. Within this broad question, Hilbert singled ou
 t the derivation of the laws of fluid mechanics (like Euler’s or Navier-Sto
 kes’ equations) by way of rigorously justifying Boltzmann’s kinetic theory 
 for particle systems. This will be the subject of our talk. The rigorous de
 rivation of Boltzmann’s kinetic equation was established for short times in
  a classic work of Lanford (1975), following inputs from Grad and Cercignan
 i. However, Hilbert’s sixth problem requires a long time version of this re
 sult. In a recent work with Yu Deng (Chicago) and Xiao Ma (Michigan), we ex
 tend Lanford’s theorem to long times; more precisely, for as long as the so
 lution of Boltzmann’s equation exists. This follows an earlier work joint w
 ork with Yu Deng that resolves a parallel problem for wave systems, where c
 olliding particles are replaced by nonlinear interacting waves.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Hilbert’s sixth problem asks for the axiomatic derivation of the laws of
  physics from first principles. Within this broad question, Hilbert singled
  out the derivation of the laws of fluid mechanics (like Euler’s or Navier-
 Stokes’ equations) by way of rigorously justifying Boltzmann’s kinetic theo
 ry for particle systems. This will be the subject of our talk. The rigorous
  derivation of Boltzmann’s kinetic equation was established for short times
  in a classic work of Lanford (1975), following inputs from Grad and Cercig
 nani. However, Hilbert’s sixth problem requires a long time version of this
  result. In a recent work with Yu Deng (Chicago) and Xiao Ma (Michigan), we
  extend Lanford’s theorem to long times; more precisely, for as long as the
  solution of Boltzmann’s equation exists. This follows an earlier work join
 t work with Yu Deng that resolves a parallel problem for wave systems, wher
 e colliding particles are replaced by nonlinear interacting waves.</p>
CONTACT:Zaher Hani (Michigan
DTSTAMP:20260828T162836
DTSTART;TZID=America/New_York:20250423T154500
DTEND;TZID=America/New_York:20250423T164500
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