The second iterate for the Navier-Stokes equation

Pierre Germain

Research output: Contribution to journalArticlepeer-review


We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak-strong uniqueness for Koch-Tataru solutions; and finally an instability result in over(B, ̇)∞, q-1, for q > 2.

Original languageEnglish (US)
Pages (from-to)2248-2264
Number of pages17
JournalJournal of Functional Analysis
Issue number9
StatePublished - Nov 1 2008


  • Bilinear operators
  • Navier-Stokes
  • Weak-strong uniqueness
  • Well-posedness

ASJC Scopus subject areas

  • Analysis


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