3 papers
math.DS2019
Stability Theory of the 3-Dimensional Euler Equations
Holger R. Dullin, Joachim Worthington
The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We show that the linearised system around these steady states decomposes into…
math.SP2019
Instability of unidirectional flows for the 2D -Euler equations
Holger Dullin, Yuri Latushkin, Robert Marangell +2
We study stability of unidirectional flows for the linearized 2D -Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier mo…
math-ph2018
Poisson Structure of the Three-Dimensional Euler Equations in Fourier Space
Holger R. Dullin, James D. Meiss, Joachim Worthington
We derive a simple Poisson structure in the space of Fourier modes for the vorticity formulation of the Euler equations on a three-dimensional periodic domain. This allows us to an…