We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-4, author = {Gerhard Str\"ohmer}, title = {About the decay of surface waves on viscous fluids without surface tension}, journal = {Banach Center Publications}, volume = {60}, year = {2003}, pages = {55-72}, zbl = {1057.35034}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-4} }
Gerhard Ströhmer. About the decay of surface waves on viscous fluids without surface tension. Banach Center Publications, Tome 60 (2003) pp. 55-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-4/