scholarly journals A note on the zero Mach number limit of compressible Euler equations

2005 ◽  
Vol 133 (10) ◽  
pp. 3079-3085 ◽  
Author(s):  
Wen-An Yong
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Zero Mach Number Limit

The Zero-Mach Limit of Compressible Euler Equations

2013 ◽  
Vol 275-277 ◽  
pp. 518-521
Author(s):  
Shu Wang
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Initial Velocity ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Compressible Euler Equations ◽  
Time Interval ◽  
Compressible Euler ◽  
Three Space ◽  
Incompressible Euler

The aim of this paper is to prove that compressible Euler equations in two and three space dimensions converge to incompressible Euler equations in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the initial velocity, or the time interval. We assume instead that the incompressible flows exists and is reasonably smooth on a given time interval, and prove that compressible flows converge uniformly on that time interval.

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler

Transonic Shock Formation in a Rarefaction Riemann Problem for the 2D Compressible Euler Equations

2008 ◽  
Vol 69 (3) ◽  
pp. 720-742 ◽  
Author(s):  
James Glimm ◽  
Xiaomei Ji ◽  
Jiequan Li ◽  
Xiaolin Li ◽  
Peng Zhang ◽  
...  
Keyword(s):  
Euler Equations ◽  
Riemann Problem ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Transonic Shock ◽  
Compressible Euler

Local existence with low regularity for the 2D compressible Euler equations

2021 ◽  
Vol 18 (03) ◽  
pp. 701-728
Author(s):  
Huali Zhang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Euler Equations ◽  
Local Existence ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Spatial Derivative ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Local Solutions

We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].

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