Lower bounds on blowing-up solutions of the three-dimensional navier-stokes equations in H3/2, H5/2, and B5/22,1

David S. McCormick, Eric J. Olson, James C. Robinson, Jose L. Rodrigo, Alejandro Vidal-Lopez, Yi Zhou

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7 Citations (Scopus)


If u is a smooth solution of the Navier-Stokes equations on with first blowup time T, we prove lower bounds for u in the Sobolev spaces and the Besov space with optimal rates of blowup: we prove the strong lower bounds and we obtain lim sup c, a weaker result. The proofs involve new inequalities for the nonlinear term in Sobolev and Besov spaces, both of which are obtained using a dyadic decomposition of u.

Original languageEnglish
Pages (from-to)2119-2132
Number of pages14
JournalSIAM Journal on Mathematical Analysis
Issue number3
Publication statusPublished - 2016


  • Blowup
  • Commutator estimates
  • Navier-Stokes equations

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