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# 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} }

- Published 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