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 over(B, ̇)∞, q-1, for q > 2.
Original language | English (US) |
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Pages (from-to) | 2248-2264 |
Number of pages | 17 |
Journal | Journal of Functional Analysis |
Volume | 255 |
Issue number | 9 |
DOIs | |
State | Published - Nov 1 2008 |
Keywords
- Bilinear operators
- Navier-Stokes
- Weak-strong uniqueness
- Well-posedness
ASJC Scopus subject areas
- Analysis