We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as , where is the viscosity coefficient.
@incollection{JEDP_2008____A8_0,
author = {Sueur, Franck},
title = {Vorticity internal transition layers for the {Navier-Stokes} equations},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {8},
pages = {1--15},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2008},
doi = {10.5802/jedp.52},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.52/}
}
TY - JOUR AU - Sueur, Franck TI - Vorticity internal transition layers for the Navier-Stokes equations JO - Journées équations aux dérivées partielles PY - 2008 SP - 1 EP - 15 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.52/ DO - 10.5802/jedp.52 LA - en ID - JEDP_2008____A8_0 ER -
%0 Journal Article %A Sueur, Franck %T Vorticity internal transition layers for the Navier-Stokes equations %J Journées équations aux dérivées partielles %D 2008 %P 1-15 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.52/ %R 10.5802/jedp.52 %G en %F JEDP_2008____A8_0
Sueur, Franck. Vorticity internal transition layers for the Navier-Stokes equations. Journées équations aux dérivées partielles (2008), article no. 8, 15 p. doi : 10.5802/jedp.52. http://www.numdam.org/articles/10.5802/jedp.52/
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