scholarly journals Incompressible limit of Euler equations with damping

2021 ◽  
Vol 30 (1) ◽  
pp. 126-139
Author(s):  
Fei Shi ◽  
Keyword(s):  
Cauchy Problem ◽  
Mach Number ◽  
Euler System ◽  
Existence Results ◽  
Incompressible Limit ◽  
Low Mach Number ◽  
Uniform Estimates ◽  
Low Mach Number Limit ◽  
Compressible Euler ◽  
The Cauchy Problem

<abstract><p>The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.</p></abstract>

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.

scholarly journals On the Low Mach Number Limit for the Compressible Euler System

2019 ◽  
Vol 51 (2) ◽  
pp. 1496-1513 ◽  
Author(s):  
Eduard Feireisl ◽  
Christian Klingenberg ◽  
Simon Markfelder
Keyword(s):  
Mach Number ◽  
Euler System ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Compressible Euler

scholarly journals Global existence of a radiative Euler system coupled to an electromagnetic field

2018 ◽  
Vol 8 (1) ◽  
pp. 1158-1170
Author(s):  
Xavier Blanc ◽  
Bernard Ducomet ◽  
Šárka Nečasová
Keyword(s):  
Cauchy Problem ◽  
Electromagnetic Field ◽  
Global Existence ◽  
Smooth Solution ◽  
Euler System ◽  
Singular Limit ◽  
System Of Equations ◽  
Global Smooth Solution ◽  
Compressible Euler ◽  
The Cauchy Problem

Abstract We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely, the 3D radiative compressible Euler system coupled to an electromagnetic field. Assuming smallness hypotheses for the data, we prove that the problem admits a unique global smooth solution and study its asymptotics.

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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