Global $${{\dot{H}^1 \cap \dot{H}^{-1}}}$$ H ˙ 1 ∩ H ˙ - 1 Solutions to a Logarithmically Regularized 2D Euler Equation

2014 ◽  
Vol 17 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Hongjie Dong ◽  
Dong Li
Keyword(s):  
Euler Equation ◽  
2D Euler Equation

On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition

2016 ◽  
Vol 73 (3) ◽  
pp. 523-544 ◽  
Author(s):  
Igor Kukavica ◽  
Amjad Tuffaha ◽  
Vlad Vicol ◽  
Fei Wang
Keyword(s):  
Euler Equation ◽  
Free Interface ◽  
2D Euler Equation

scholarly journals Stochastic stability of invariant measures: The 2D Euler equation

2019 ◽  
Vol 33 (17) ◽  
pp. 1950185
Author(s):  
F. Cipriano ◽  
H. Ouerdiane ◽  
R. Vilela Mendes
Keyword(s):  
Euler Equation ◽  
Coherent Structures ◽  
Stochastic Stability ◽  
Invariant Measures ◽  
Finite Dimensional ◽  
Stochastically Stable ◽  
2D Euler Equation ◽  
Stable Measures ◽  
Dissipative Dynamical Systems ◽  
Selection Of

In finite-dimensional dissipative dynamical systems, stochastic stability provides the selection of the physically relevant measures. That this might also apply to systems defined by partial differential equations, both dissipative and conservative, is the inspiration for this work. As an example, the 2D Euler equation is studied. Among other results this study suggests that the coherent structures observed in 2D hydrodynamics are associated with configurations that maximize stochastically stable measures uniquely determined by the boundary conditions in dynamical space.

scholarly journals Quasilinear Theory of the 2D Euler Equation

2000 ◽  
Vol 84 (24) ◽  
pp. 5512-5515 ◽  
Author(s):  
Pierre-Henri Chavanis
Keyword(s):  
Euler Equation ◽  
Quasilinear Theory ◽  
2D Euler Equation
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