Viscous profiles of vortex patches. (January 2015)

• Record Type: Journal Article
• Authors: Sueur, Franck
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 14:Number 1(2015:Jan.)
• Page Start: 1
• Page End: 68
• Publication Date: 2015-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748013000285
• Languages: English
• ISSNs: 1474-7480

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>We deal with the incompressible Navier–Stokes equations with vortex patches as initial data. Such data describe an initial configuration for which the vorticity is discontinuous across a hypersurface. We give an asymptotic expansion of the solutions in the vanishing viscosity limit which exhibits an internal layer where the fluid vorticity has a sharp variation. This layer moves with the flow of the Euler equations.</p> </abstract>