# On the stabilizing effect of rotation in the 3d Euler equations

@article{Guo2020OnTS, title={On the stabilizing effect of rotation in the 3d Euler equations}, author={Yan Guo and Chunyan Huang and Benoit Pausader and Klaus Widmayer}, journal={arXiv: Analysis of PDEs}, year={2020} }

While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Euler equations in $\mathbb{R}^3$ with a fixed speed of rotation. We show that for any $M>0$, axisymmetric initial data of sufficiently small size $\varepsilon$ lead to solutions that exist for a long time at least $\varepsilon^{-M}$ and disperse. This…

## One Citation

Global Axisymmetric Euler Flows with Rotation

- Mathematics
- 2021

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform “rigid body” rotation. These solutions are axisymmetric, of Sobolev…

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