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Comportement en temps long des fluides visqueux bidimensionnels.

Abstract : This report investigates the long-time asymptotic behaviour of viscous bidimensional fluids, either homogeneous or weakly-inhomogeneous. Regarding homogeneous fluids, Thierry Gallay and C. Eugene Wayne have shown the major role of a family of self-similar solutions, the Oseen vortices, which attracts any solution of the Navier-Stokes equation with a finite measure as initial vorticity and non-zero circulation. Their result is non-explicit and the first task of this report is to make it explicit, getting this way a bound for the time-life of bidimensional turbulence. Then is shown the asymptotic stability of the Oseen vortices as density-dependent fluids, which also enables one to recover the result of Gallay and Wayne for slow weakly-inhomogeneous incompressible fluids. At last, it is proved that slow weakly-inhomogeneous compressible fluids, with zero circulation, behave asymptotically mainly as homogeneous fluids.
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https://tel.archives-ouvertes.fr/tel-00200818
Contributor : Luis Miguel Rodrigues <>
Submitted on : Friday, December 21, 2007 - 5:41:43 PM
Last modification on : Wednesday, November 4, 2020 - 1:46:59 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 2:57:09 PM

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  • HAL Id : tel-00200818, version 1

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Luis Miguel Rodrigues. Comportement en temps long des fluides visqueux bidimensionnels.. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2007. Français. ⟨tel-00200818⟩

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