Existence and stability theorems for abstract parabolic equations, and some of their applications
Volume 33 / 1996
Banach Center Publications 33 (1996), 369-382
DOI: 10.4064/-33-1-369-382
Abstract
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
