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The second iterate for the Navier–Stokes equation

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
255
Issue
9
Identifiers
DOI: 10.1016/j.jfa.2008.07.014
Keywords
  • Navier–Stokes
  • Well-Posedness
  • Weak–Strong Uniqueness
  • Bilinear Operators

Abstract

Abstract 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 B ˙ ∞ , q −1 , for q > 2 .

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