On local uniqueness of weak solutions to the navier-stokes system with BMO -1 initial datum

Igor Kukavica; Vlad Vicol

doi:10.1007/s10884-008-9116-3

On local uniqueness of weak solutions to the navier-stokes system with BMO ^-1 initial datum

Igor Kukavica
, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We address the problem of local uniqueness of weak solutions to the Navier-Stokes system, with the initial datum in a subspace of BMO ^-1ℝⁿ). The existence and uniqueness of local mild solutions has been proven by Koch and Tataru (Adv Math 157:22-35, 2001). We present a necessary and sufficient condition for two weak solutions to evolve from the same initial datum, and for weak solutions to be mild.

Original language	English (US)
Pages (from-to)	719-732
Number of pages	14
Journal	Journal of Dynamics and Differential Equations
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s10884-008-9116-3
State	Published - Sep 2008

All Science Journal Classification (ASJC) codes

Analysis

Keywords

BMO
Mild solutions
Navier-Stokes equations
Uniqueness
Weak solutions

Access to Document

10.1007/s10884-008-9116-3

Cite this

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abstract = "We address the problem of local uniqueness of weak solutions to the Navier-Stokes system, with the initial datum in a subspace of BMO -1ℝn). The existence and uniqueness of local mild solutions has been proven by Koch and Tataru (Adv Math 157:22-35, 2001). We present a necessary and sufficient condition for two weak solutions to evolve from the same initial datum, and for weak solutions to be mild.",

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KW - Navier-Stokes equations

KW - Uniqueness

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