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arXiv · 1311.0934

The two-dimensional Euler equations in Yudovich type space and $\mathrm{\textbf{bmo}}$-type space

Qionglei Chen·Changxing Miao·Xiaoxin Zheng
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Abstract

We construct global-in-time, unique solutions of the two-dimensional Euler equations in a Yudovich type space and a $\rm bmo$-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.

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Qionglei Chen, Changxing Miao, Xiaoxin Zheng. 2019-01-10. The two-dimensional Euler equations in Yudovich type space and $\mathrm{\textbf{bmo}}$-type space. https://doi.org/10.4171/rmi%2F1053

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