Well-Posedness and Uniform Bounds for a Nonlocal Third Order Evolution Operator on an Infinite Wedge

@inproceedings{Knpfer2011WellPosednessAU,
  title={Well-Posedness and Uniform Bounds for a Nonlocal Third Order Evolution Operator on an Infinite Wedge},
  author={Hans Kn{\"u}pfer and Nader Masmoudi},
  year={2011}
}
We investigate regularity and well-posedness for a fluid evolution model in the presence of a three-phase contact point. We consider a fluid evolution governed by Darcy’s Law. After linearization, we obtain a nonlocal third order operator which contains the Dirichlet-Neumann operator on the wedge with opening angle > 0. We show well-posedness and regularity for this linear evolution equation. In the limit of vanishing opening angle, we show the convergence of solutions to a fourth order… CONTINUE READING