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

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 383-419
- ISSN: 0137-6934

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topRodolfo 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 -

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