Uniqueness of the particle trajectories of the weak solutions of the two-dimensional Navier-Stokes equations ⋆

@inproceedings{Dashti2008UniquenessOT,
  title={Uniqueness of the particle trajectories of the weak solutions of the two-dimensional Navier-Stokes equations ⋆},
  author={Masoumeh Dashti and James C. Robinson},
  year={2008}
}
We address the problem of the uniqueness of the particle trajectories corresponding to a weak solution of the two-dimensional Navier-Stokes equations with square integrable initial condition and regular enough forcing function. In order to do this we obtain an estimate for H-norm of the weak solutions of the Navier-Stokes equations and show that t‖D3/2u‖ is bounded which provides a bound on the time derivative of the corresponding trajectories near the initial time. This, combined with an… CONTINUE READING