A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations (Q5930687)
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scientific article; zbMATH DE number 1590230
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations |
scientific article; zbMATH DE number 1590230 |
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A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations (English)
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23 April 2001
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compressible Navier-Stokes equations
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periodic solutions
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Mach number
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weakly compressible
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The author studies periodic solutions of the weakly compressible Navier-Stokes equations for small Mach numbers. The main results of the paper are: NEWLINENEWLINENEWLINE(i) If the initial velocity satisfies a smallness condition in terms of the viscosity, then the system has a smooth solution for all \(T > 0.\)NEWLINENEWLINENEWLINE(ii) As the Mach number tends to zero, the solution of the compressible system approaches the solution of the incompressible Navier-Stokes equations plus a term which represents the fast waves.
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