Uniqueness of mild solutions of the Navier-Stokes system in LN

P. L. Lions; N. Masmoudi

doi:10.1081/PDE-100107819

Uniqueness of mild solutions of the Navier-Stokes system in L^N

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Abstract

We prove the uniqueness of mild solutions and very 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 double-struck T sign^N with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a "dual" problem, a decomposition of the solutions and a "bootstrap" argument.

Original language	English (US)
Pages (from-to)	2211-2226
Number of pages	16
Journal	Communications in Partial Differential Equations
Volume	26
Issue number	11-12
DOIs	https://doi.org/10.1081/PDE-100107819
State	Published - 2001

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1081/PDE-100107819

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abstract = "We prove the uniqueness of mild solutions and very 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 double-struck T signN with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a {"}dual{"} problem, a decomposition of the solutions and a {"}bootstrap{"} argument.",

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AU - Masmoudi, N.

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AB - We prove the uniqueness of mild solutions and very 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 double-struck T signN with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a "dual" problem, a decomposition of the solutions and a "bootstrap" argument.

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Uniqueness of mild solutions of the Navier-Stokes system in L^N

Abstract

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