On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion

Rodolfo Salvi. "On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion." Banach Center Publications 81.1 (2008): 383-419. <http://eudml.org/doc/281657>.

@article{RodolfoSalvi2008,
abstract = {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 $L^q$-maximal regularity is investigated.},
author = {Rodolfo Salvi},
journal = {Banach Center Publications},
keywords = {incompressible Navier-Stokes equations; mass diffusion; weak solution; strong solution; maximal regularity},
language = {eng},
number = {1},
pages = {383-419},
title = {On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion},
url = {http://eudml.org/doc/281657},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Rodolfo Salvi
TI - On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 383
EP - 419
AB - 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 $L^q$-maximal regularity is investigated.
LA - eng
KW - incompressible Navier-Stokes equations; mass diffusion; weak solution; strong solution; maximal regularity
UR - http://eudml.org/doc/281657
ER -