Wellposedness and Norm Inflation for the Navier-Stokes Equations in Anisotropic Spaces

par Kenji Nakanishi (RIMS, Kyoto University & IHES)

jeudi 30 avr. 2026, 14:00 → 15:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire d'Analyse

This 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 illposedness by norm inflation everywhere in the function space. Another endpoint of subcritical case is shown to be illposed by discontinuity everywhere of the solution map. Asymptotic profile of the inflation is given in terms of the linearized instability of the Kolmogorov flows for the Euler equation. We also give a full rigorous description of its spectra in two space dimensions.

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