# Wydawnictwa / Banach Center Publications / Wszystkie tomy

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

### Tom 81 / 2008

Banach Center Publications 81 (2008), 383-419 MSC: Primary 35Q30; Secondary 76D03. DOI: 10.4064/bc81-0-24

#### Streszczenie

This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in $R^3$ with $C^3$ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter $\lambda \rightarrow 0.$ Moreover, the existence of $L^2$-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.

#### Autorzy

• Rodolfo SalviDepartment of Mathematics
Politecnico di Milano
P.zza L. da Vinci
20133 Milan, Italy
e-mail

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