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arXiv · 2109.05286

Remarks on the solution map for Yudovich solutions of the Euler equations

Huy Q. Nguyen
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Abstract

Consider Yudovich solutions to the incompressible Euler equations with bounded initial vorticity in bounded planar domains or in $\mathbb{R}^2$. We present a purely Lagrangian proof that the solution map is strongly continuous in $L^p$ for all $p\in [1, \infty)$ and is weakly-$*$ continuous in $L^\infty$.

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Huy Q. Nguyen. 2021-09-11. Remarks on the solution map for Yudovich solutions of the Euler equations. https://doi.org/10.1007/s00021-022-00678-3

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