Corpus ID: 202749842

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

  title={Local Hadamard well-posedness results for the Navier-Stokes equations.},
  author={Tobias Barker},
  journal={arXiv: Analysis of PDEs},
  • 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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