Time-asymptotic behavior of solutions for general Navier-Stokes equations in even space-dimension (Q2712157)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Time-asymptotic behavior of solutions for general Navier-Stokes equations in even space-dimension |
scientific article |
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18 March 2002
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weak Huygens' principle
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time-dependent compressible Navier-Stokes equations
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Duhamel principle
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pointwise estimates of the Green function
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linearized system
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existence
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uniqueness
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global in time classical solution
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integral time-asymptotic estimates
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Cauchy problem
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Time-asymptotic behavior of solutions for general Navier-Stokes equations in even space-dimension (English)
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The author studies the time-asymptotic behaviour of solutions to general time-dependent compressible Navier-Stokes equations in even, higher than two, space dimensions. The proof is based on the use of Duhamel principle and on pointwise estimates of the Green function for a linearized system. This allows to establish the existence and uniqueness of a global-in-time classical solution, and to give Schauder-type integral time-asymptotic estimates of the solutions to the Cauchy problem for original nonlinear system. The result can be interpreted as a weak modification of Huygens' principle.
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