Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to , and pressure belongs to for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-7,
author = {Wisam Alame},
title = {On existence of solutions for the nonstationary Stokes system with boundary slip conditions},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {195-223},
zbl = {1075.35028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-7}
}
Wisam Alame. On existence of solutions for the nonstationary Stokes system with boundary slip conditions. Applicationes Mathematicae, Tome 32 (2005) pp. 195-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-2-7/