scholarly journals Well-posedness of the 2D Euler equations when velocity grows at infinity

2019 ◽  
Vol 39 (5) ◽  
pp. 2361-2392
Author(s):  
Elaine Cozzi ◽  
◽  
James P. Kelliher ◽  
Keyword(s):  
Euler Equations ◽  
Well Posedness ◽  
2D Euler Equations

scholarly journals The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint
Keyword(s):  
Euler Equation ◽  
Function Space ◽  
Euler Equations ◽  
Small Perturbation ◽  
Function Spaces ◽  
Well Posedness ◽  
Small Solution ◽  
Null Solution ◽  
Linearized Euler Equations ◽  
The Stability

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

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