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

100%

Salvi R.

Banach Center Publications

2008

tom 81

nr 1

383-419

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.

Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains

100%

Salvi R.

Banach Center Publications

2005

tom 70

nr 1

209-237

In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence of a weak solution is treated.

Ograniczanie wyników

2 Banach Center Publications

2 Salvi R.

1 2008

1 2005

Wyniki wyszukiwania

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

Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains