Interactions of Rarefaction Waves and Rarefaction Shocks of the Two-Dimensional Compressible Euler Equations with General Equation of State

2021 ◽  
Author(s):  
Geng Lai
Keyword(s):  
Equation Of State ◽  
Euler Equations ◽  
General Equation ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Rarefaction Waves ◽  
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].

scholarly journals Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations

2018 ◽  
Vol 15 (04) ◽  
pp. 721-730 ◽  
Author(s):  
Christian Klingenberg ◽  
Simon Markfelder
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Weak Solutions ◽  
Gas Dynamics ◽  
Energy Inequality ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Energy Equality ◽  
Compressible Euler ◽  
Appl Math

We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.

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