Decay in time of incompressible flows (Q1402387)
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scientific article; zbMATH DE number 1971867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decay in time of incompressible flows |
scientific article; zbMATH DE number 1971867 |
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Decay in time of incompressible flows (English)
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27 August 2003
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The authors examine the Cauchy problem for incompressible Navier-Stokes or MHD equations with initial data given on all space. They give a proof for the time decay of the spatial \(L_2\)-norm of the solution, under the assumption that the solution of the heat equation with the same initial data decays. The proof is based on a decay estimate for the first derivatives of the solution, Duhamel's principle, and Gronwall-type arguments.
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Navier-Stokes equations
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MHD equations
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Gronwall lemma
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Cauchy problem
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heat equation
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Duhamel's principle
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