@article{Chemin2025, 
author = {Jean-Yves Chemin},
title = {Non linear equivalence of some scaling invariant norms for solutions of incompressible Navier-Stokes equations},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {4},
pages = {944-954},
keywords = {incompressible Navier-Stokes, Besov spaces},
url = {https://www.sciopen.com/article/10.3934/cam.2025038},
doi = {10.3934/cam.2025038},
abstract = {Motivated by the study of the possible breakdown of regularity for solutions of the incompressible Navier-Stokes system in the whole three-dimensional space                                            R                                          3  , we prove that the norm    ‖  u      ‖                  L        T        ∞            (              B                  2          ∞                                      1            2                              )       and the quantity        sup          I      ⊂      [      0      ,      T      [            1                  |            I              |                  ∫          I        ‖  ∇  u  (  t  )      ‖                  L        2              2    d  t are non linearly equivalent. The proofs rely on the Duhamel formula, dyadic localization in the Fourier space, and for one of them, on the energy inequality.}
}