Differential and Integral Equations

Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations

Isabelle Gallagher

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Abstract

We consider the Navier--Stokes equations in~$\mathbb R^3$, in an axisymmetric setting: the data and the solutions only depend on the radial and on the vertical variable. In [7], a unique solution is constructed in a scale invariant function space~$L^2_0$, equivalent to~$L^2$ at finite distance from the vertical axis. We prove here a weak--strong uniqueness result for such solutions associated with data in~$L^2 \cap L^2_0$.

Article information

Source
Differential Integral Equations, Volume 16, Number 5 (2003), 557-572.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060626

Mathematical Reviews number (MathSciNet)
MR1973062

Zentralblatt MATH identifier
1161.76456

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30]
Secondary: 35B35: Stability 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76E99: None of the above, but in this section

Citation

Gallagher, Isabelle. Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations. Differential Integral Equations 16 (2003), no. 5, 557--572. https://projecteuclid.org/euclid.die/1356060626


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