Vanishing viscosity limit for a system of balance laws with general type initial data arising from 1D Saint-Venant model

2020 ◽  
Vol 61 (5) ◽  
pp. 051507
Author(s):  
Manas R. Sahoo ◽  
Abhrojyoti Sen
Keyword(s):  
Initial Data ◽  
General Type ◽  
Balance Laws ◽  
Vanishing Viscosity ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
System Of Balance Laws

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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