Stability in \(L^ r\) for the Navier-Stokes flow in an \(n\)-dimensional bounded domain (Q2638869)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability in \(L^ r\) for the Navier-Stokes flow in an \(n\)-dimensional bounded domain |
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Stability in \(L^ r\) for the Navier-Stokes flow in an \(n\)-dimensional bounded domain (English)
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1990
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The paper deals with the uniqueness of solutions to a boundary value problem and an initial-boundary value problem for the Navier-Stokes equations, respectively. If the external force and the initial condition are in \(L^ 2(\Omega)\), where \(\Omega\) is a bounded domain in \({\mathbb{R}}^ n\), the two considered problems have a unique solution. The proofs are based on a method due to \textit{Y. Giga} and \textit{T. Miyakawa} [Arch. Ration. Mech. Anal. 89, 267-281 (1985; Zbl 0587.35078)].
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uniqueness of solutions
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boundary value problem
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initial-boundary value problem
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Navier-Stokes equations
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unique solution
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