Corpus ID: 202749842

# Local Hadamard well-posedness results for the Navier-Stokes equations.

@article{Barker2019LocalHW,
title={Local Hadamard well-posedness results for the Navier-Stokes equations.},
author={Tobias Barker},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Tobias Barker
• Published 2019
• Mathematics
• arXiv: Analysis of PDEs
• In this paper we consider classes of initial data that ensure local-in-time Hadamard well-posedness of the associated weak Leray-Hopf solutions of the three-dimensional Navier-Stokes equations. In particular, for any solenodial $L_{2}$ initial data $u_{0}$ belonging to certain subsets of $VMO^{-1}(\mathbb{R}^3)$, we show that weak Leray-Hopf solutions depend continuously with respect to small divergence-free $L_{2}$ perturbations of the initial data $u_{0}$ (on some finite-time interval). Our… CONTINUE READING

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