Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L1 Vorticity

@article{Crippa2017EulerianAL,
  title={Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L1 Vorticity},
  author={Gianluca Crippa and Camilla Nobili and Christian Seis and Stefano Spirito},
  journal={SIAM J. Math. Anal.},
  year={2017},
  volume={49},
  pages={3973-3998}
}
In the first part of this paper we establish a uniqueness result for continuity equations with velocity field whose derivative can be represented by a singular integral operator of an $L^1$ function, extending the Lagrangian theory in \cite{BouchutCrippa13}. The proof is based on a combination of a stability estimate via optimal transport techniques developed in \cite{Seis16a} and some tools from harmonic analysis introduced in \cite{BouchutCrippa13}. In the second part of the paper, we address… 
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