Uniqueness of weak solutions of the navier-stokes equations in ln(Ω)

Pierre Louis Lions; Nader Masmoudi

doi:10.1016/S0764-4442(99)80028-7

Uniqueness of weak solutions of the navier-stokes equations in lⁿ(Ω)

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Abstract

We prove the uniqueness of weak solutions of the Navier-Stokes equations in C([0, T); L^N(Ω)), where Ω is the whole space ℝ^N, a regular domain of ℝ^N or the torus T^N , with N ≥ 3. The proof lies on three elementary ingredients: the introduction of a dual problem, a decomposition of the solutions and a "boostrap" argument.

Original language	English (US)
Pages (from-to)	491-496
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	327
Issue number	5
DOIs	https://doi.org/10.1016/S0764-4442(99)80028-7
State	Published - Sep 1998

ASJC Scopus subject areas

General Mathematics

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10.1016/S0764-4442(99)80028-7

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title = "Uniqueness of weak solutions of the navier-stokes equations in ln(Ω)",

abstract = "We prove the uniqueness of weak solutions of the Navier-Stokes equations in C([0, T); LN(Ω)), where Ω is the whole space ℝN, a regular domain of ℝN or the torus TN , with N ≥ 3. The proof lies on three elementary ingredients: the introduction of a dual problem, a decomposition of the solutions and a {"}boostrap{"} argument.",

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AU - Lions, Pierre Louis

AU - Masmoudi, Nader

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N2 - We prove the uniqueness of weak solutions of the Navier-Stokes equations in C([0, T); LN(Ω)), where Ω is the whole space ℝN, a regular domain of ℝN or the torus TN , with N ≥ 3. The proof lies on three elementary ingredients: the introduction of a dual problem, a decomposition of the solutions and a "boostrap" argument.

AB - We prove the uniqueness of weak solutions of the Navier-Stokes equations in C([0, T); LN(Ω)), where Ω is the whole space ℝN, a regular domain of ℝN or the torus TN , with N ≥ 3. The proof lies on three elementary ingredients: the introduction of a dual problem, a decomposition of the solutions and a "boostrap" argument.

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Uniqueness of weak solutions of the navier-stokes equations in lⁿ(Ω)

Abstract

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