The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations

2005 ◽  
Vol 83 (4-5) ◽  
pp. 267-278 ◽  
Author(s):  
Liviu Marin ◽  
Daniel Lesnic
Keyword(s):  
Cauchy Problem ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Two Dimensional ◽  
The Cauchy Problem

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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