The two-dimensional Euler equations in Yudovich type space and $\mathrm{\textbf{bmo}}$-type space
Abstract
We construct global-in-time, unique solutions of the two-dimensional Euler equations in a Yudovich type space and a -type space. First, we show the regularity of solutions for the two-dimensional Euler equations in the Spanne space involving an unbounded and non-decaying vorticity. Next, we establish an estimate with a logarithmic loss of regularity for the transport equation in a bmo-type space by developing classical analysis tool such as the John-Nirenberg inequality. We also optimize estimates of solutions to the vorticity-stream formulation of the two-dimensional Euler equations with a bi-Lipschitz vector field in bmo-type space by combining an observation introduced by Yodovich with the so-called "quasi-conformal property" of the incompressible.
Keywords
Cite
@article{arxiv.1311.0934,
title = {The two-dimensional Euler equations in Yudovich type space and $\mathrm{\textbf{bmo}}$-type space},
author = {Qionglei Chen and Changxing Miao and Xiaoxin Zheng},
journal= {arXiv preprint arXiv:1311.0934},
year = {2019}
}
Comments
39pages. Thanks Philippe Serfati for providing us with his paper: Pertes de r\'egularit\'e le laplacien et l'\'equation d'Euler sui $\mathbb R^n$, priprint.15,pp., 1994."