Precise regularity results for the Euler equations

It has already been proved, under various assumptions, that no singularity can appear in an initially regular perfect fluid flow, if the L∞ norm of the velocity’s curl does not blow up. Here that result is proved for flows in smooth bounded domains of Rd (d 2) when the regularity is expressed in terms of Besov (or Triebel–Lizorkin) spaces.  2003 Elsevier Science (USA). All rights reserved