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SUMMARY:Wellposedness and Norm Inflation for the Navier-Stokes Equations  
 in Anisotropic Spaces
DTSTART:20260430T120000Z
DTEND:20260430T133000Z
DTSTAMP:20260503T045200Z
UID:indico-event-16472@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Kenji Nakanishi (RIMS\, Kyoto University & IHES)\n\n
 Séminaire d'Analyse\nThis is joint work with Baoxiang Wang (Jimei U.) and
  Zimeng Wang (Queen U.). We study the Cauchy problem of the Navier-Stokes 
 equations in anisotropic spaces with critical or subcritical scaling. For 
 the Lebesgue spaces\, we obtain wellposedness for all exponents\, while in
  the endpoint critical cases of the Sobolev or Besov space\, we prove illp
 osedness by norm inflation everywhere in the function space. Another endpo
 int of subcritical case is shown to be illposed by discontinuity everywher
 e of the solution map. Asymptotic profile of the inflation is given in ter
 ms of the linearized instability of the Kolmogorov flows for the Euler equ
 ation. We also give a full rigorous description of its spectra in two spac
 e dimensions.\n========\nPour être informé des prochains séminaires vou
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 essage vide.\n\nhttps://indico.math.cnrs.fr/event/16472/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16472/
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