Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics
Analysis of PDEs
2009-10-28 v1
Abstract
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general initial data in two space dimensions and for small data in data in three space dimensions. The existence in three dimensions is established by studying a linearization of a relative entropy functional. We also establish the convergence to the stationary solution with a rate.
Cite
@article{arxiv.0910.4973,
title = {Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics},
author = {Rolf J. Ryham},
journal= {arXiv preprint arXiv:0910.4973},
year = {2009}
}