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@article{Crisan:2022,
author = {Crisan, D and Holm, DD and Leahy, J-M and Nilssen, T},
journal = {arXiv},
title = {Solution properties of the incompressible Euler system with rough path advection},
url = {http://arxiv.org/abs/2104.14933v1},
year = {2022}
}

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TY  - JOUR
AB  - We consider the Euler equations for the incompressible flow of an ideal fluidwith an additional rough-in-time, divergence-free, Lie-advecting vector field.In recent work, we have demonstrated that this system arises from Clebsch andHamilton-Pontryagin variational principles with a perturbative geometric roughpath Lie-advection constraint. In this paper, we prove local well-posedness ofthe system in $L^2$-Sobolev spaces $H^m$ with integer regularity $m\ge \lfloord/2\rfloor+2$ and establish a Beale-Kato-Majda (BKM) blow-up criterion in termsof the $L^1_tL^\infty_x$-norm of the vorticity. In dimension two, we show thatthe $L^p$-norms of the vorticity are conserved, which yields globalwell-posedness and a Wong-Zakai approximation theorem for the stochasticversion of the equation.
AU  - Crisan,D
AU  - Holm,DD
AU  - Leahy,J-M
AU  - Nilssen,T
PY  - 2022///
TI  - Solution properties of the incompressible Euler system with rough path advection
T2  - arXiv
UR  - http://arxiv.org/abs/2104.14933v1
UR  - http://hdl.handle.net/10044/1/95338
ER  -

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