Evolution of the Singularities of the Schwarz Function Corresponding to the Motion of a Vortex Patch in the Two-dimensional Euler Equations

2021 ◽  
Vol 26 (5) ◽  
pp. 562-575
Author(s):  
Giorgio Riccardi ◽  
David G. Dritschel
Keyword(s):  
Euler Equations ◽  
Two Dimensional ◽  
Schwarz Function ◽  
Vortex Patch

scholarly journals New families of vortex patch equilibria for the two-dimensional Euler equations

2017 ◽  
Vol 29 (12) ◽  
pp. 123602 ◽  
Author(s):  
B. B. Xue ◽  
E. R. Johnson ◽  
N. R. McDonald
Keyword(s):  
Euler Equations ◽  
Two Dimensional ◽  
Vortex Patch

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

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 Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

2019 ◽  
Vol 266 (9) ◽  
pp. 5397-5430 ◽  
Author(s):  
Alessandro Morando ◽  
Paola Trebeschi ◽  
Tao Wang
Keyword(s):  
Euler Equations ◽  
Nonlinear Stability ◽  
Two Dimensional ◽  
Vortex Sheets
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