This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory, the problem of the -maximal regularity is investigated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-24,
author = {Rodolfo Salvi},
title = {On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {383-419},
zbl = {1154.35421},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-24}
}
Rodolfo Salvi. On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion. Banach Center Publications, Tome 83 (2008) pp. 383-419. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-24/