scholarly journals Vanishing Viscosity Limit of the Compressible Navier--Stokes Equations with General Pressure Law

2019 ◽  
Vol 51 (3) ◽  
pp. 2168-2205 ◽  
Author(s):  
Matthew R. I. Schrecker ◽  
Simon Schulz
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit

Viscous profiles of vortex patches

2013 ◽  
Vol 14 (1) ◽  
pp. 1-68 ◽  
Author(s):  
Franck Sueur
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Euler Equations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
Sharp Variation

AbstractWe 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.

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