Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations

Hideo Kozono, Yukihiro Shimada

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53 Citations (Scopus)


We shall show that every strong solution u(t) of the Navier-Stokes equations on (0, T) can be continued beyond t > T provided u ε L2/1-α (0, T; Ḟ∞∞) for 0 < α < 1, where Ḟp, qs denotes the homogeneous Triebel-Lizorkin space. As a byproduct of our continuation theorem, we shall generalize a well-known criterion due to Serrin on regularity of weak solutions. Such a bilinear estimate Ḟp1, q1 ∩ Ḟp2, q2s+α ⊂ Ḟ p, qs, 1/p = 1/p1 + I/p2, 1/q = 1/q1 + 1/q2 as the Hölder type inequality plays an important role for our results.

Original languageEnglish
Pages (from-to)63-74
Number of pages12
JournalMathematische Nachrichten
Publication statusPublished - 2004 Jan 1



  • Littlewood-Paley decomposition
  • Navier-Stokes equations
  • Triebel-Lizorkin space

ASJC Scopus subject areas

  • Mathematics(all)

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