$$L^{1}$$ convergences and convergence rates of approximate solutions for compressible Euler equations near vacuum

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Hsin-Yi Lee ◽  
Jay Chu ◽  
John M. Hong ◽  
Ying-Chieh Lin
Keyword(s):  
Euler Equations ◽  
Convergence Rates ◽  
Approximate Solutions ◽  
Compressible Euler Equations ◽  
Compressible Euler

GLOBAL SOLUTIONS TO THE COMPRESSIBLE EULER EQUATIONS WITH GRAVITATIONAL SOURCE

2008 ◽  
Vol 05 (02) ◽  
pp. 317-346 ◽  
Author(s):  
NAOKI TSUGE
Keyword(s):  
Euler Equations ◽  
Global Solutions ◽  
Approximate Solutions ◽  
Compressible Euler Equations ◽  
Godunov Scheme ◽  
Compressible Euler ◽  
Gravitational Source ◽  
Solid Ball ◽  
Physical Importance ◽  
Norm Bound

We study the compressible Euler equations in spherical symmetry with a gravitational source surrounding a solid ball. Despite its physical importance, this problem has not received much attention until now. We prove the global existence of weak solutions by constructing approximate solutions and using a modified Godunov scheme. The main point is to obtain a sup-norm bound for the approximate solutions.

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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