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• # Artykuł - szczegóły

## Banach Center Publications

2008 | 81 | 1 | 383-419

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

EN

### Abstrakty

EN
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.

383-419

wydano
2008

### Twórcy

autor
• Department of Mathematics, Politecnico di Milano, P.zza L. da Vinci, 20133 Milan, Italy