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2003 Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations
Isabelle Gallagher
Differential Integral Equations 16(5): 557-572 (2003).

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~$L^2 \cap L^2_0$.

Citation

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Isabelle Gallagher. "Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations." Differential Integral Equations 16 (5) 557 - 572, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1161.76456
MathSciNet: MR1973062

Subjects:
Primary: 76D05
Secondary: 35B35, 35Q30, 76D03, 76E99

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 5 • 2003
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