The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces (Q2504027)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces |
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The initial-value problem for the Navier-Stokes equations with a free surface in \(L^q\)-Sobolev spaces (English)
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22 September 2006
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The author deals with the time-dependent flow of an incompressible, viscous fluid bounded above by a free surface and below by a fixed bottom under the influence of gravity. The author shows short-time existence of strong solutions of this free-boundary problem in the setting of anisotropic \(L^q\)-Sobolev spaces for \(q> n\) in space dimension \(n\geq 2\).
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free surface
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anisotropic Sobolev space
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strong solution
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short-time existence
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