Two-Dimensional Euler System and the Vortex Patches Problem

2005 ◽  
pp. 83-160
Author(s):  
Jean-Yves Chemin
Keyword(s):  
Euler System ◽  
Two Dimensional

Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

2014 ◽  
Vol 144 (6) ◽  
pp. 1127-1154 ◽  
Author(s):  
Taoufik Hmidi ◽  
Samira Sulaiman
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Euler System ◽  
Incompressible Limit ◽  
Two Dimensional ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Critical Besov Space ◽  
Convergence Results ◽  
Incompressible Euler

We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

Instability of Shielded Surface Temperature Vortices

2011 ◽  
Vol 68 (5) ◽  
pp. 964-971 ◽  
Author(s):  
Benjamin J. Harvey ◽  
Maarten H. P. Ambaum ◽  
Xavier J. Carton
Keyword(s):  
Surface Temperature ◽  
Smooth Surface ◽  
Numerical Study ◽  
Normal Modes ◽  
Euler System ◽  
The Other ◽  
Two Dimensional ◽  
Dynamics Model ◽  
Contour Dynamics ◽  
The Stability

Abstract The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

scholarly journals On two-dimensional Riemann problem for pressure-gradient equations of the Euler system

1998 ◽  
Vol 4 (4) ◽  
pp. 609-634 ◽  
Author(s):  
Peng Zhang ◽  
◽  
Jiequan Li ◽  
Tong Zhang ◽  
◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Riemann Problem ◽  
Euler System ◽  
Two Dimensional ◽  
Pressure Gradient Equations
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