Small scale creation for solutions of the incompressible two dimensional Euler equation
By Alexander V. Kiselev, Vladimír Sverák. 2013
290 citations recorded by the source corpus.
We construct an initial data for two-dimensional Euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times. This estimate is known to be sharp - the double exponential growth is the fastest possible growth rate.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/6df7ade32a22705c47669d14355207c05dad1906
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In Applied Mathematics
- Tarek M. Elgindi
- Andrej Zlatoš
- In-Jee Jeong
- Yao Yao
- Lenya Ryzhik
- Zhifei Zhang
- Dongyi Wei
- Weiren Zhao
In Computational Mechanics
- Andrej Zlatoš
- Yao Yao
- Lenya Ryzhik
- Tarek M. Elgindi
- Alexander V. Kiselev
- Zhifei Zhang
- Weiren Zhao
- Dongyi Wei
Citations in the corpus
- Ill-posedness for the Incompressible Euler Equations in Critical Sobolev Spaces (2016, background): “Let (ω, u,Φ) to be the solution triple for the 2D Euler equations in T2 with initial data ω0.”
- Finite time singularity for the modified SQG patch equation (2016, methodology): “As we have mentioned above, our choice of initial data is motivated by the numerical simulations of the threedimensional Euler equations in [40], [39], as well as by the example of smooth solutions to the 2D Euler equations with a double exponential temporal growth of their vorticity gradients in [3”
- Linear Inviscid Damping for a Class of Monotone Shear Flow in Sobolev Spaces (2015, result): “We refer to [8, 11] for recent relevant results.”