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

• Autorzy: Rodolfo Salvi
• Języki publikacji: 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.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 383-419

Daty

wydano

2008

Twórcy

autor

Rodolfo Salvi

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

Identyfikatory

DOI

10.4064/bc81-0-24