Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 7

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Existence of solutions vanishing near some axis for the nonstationary Stokes system with boundary slip conditions

100%
Zajączkowski W.
Instytut Matematyczny Polskiej Akademii Nauk
EN
We examine the nonstationary Stokes system in a bounded domain with the boundary slip conditions. We assume that there exists a line which crosses the domain and that the data belong to Sobolev spaces with weights equal to some powers of the distance to the line. Then the existence of solutions in Sobolev spaces with the corresponding weights is proved.
2
Content available remote

Long time existence of regular solutions to Navier-Stokes equations in cylindrical domains under boundary slip conditions

95%
Zajączkowski W.
Studia Mathematica
|
2005
|
tom 169
|
nr 3
243-285
EN
Long time existence of solutions to the Navier-Stokes equations in cylindrical domains under boundary slip conditions is proved. Moreover, the existence of solutions with no restrictions on the magnitude of the initial velocity and the external force is shown. However, we have to assume that the quantity $I = ∑_{i=1}^{2} (||∂_{x₃}^{i} v(0)||_{L₂(Ω)} + ||∂_{x₃}^{i}f||_{L₂(Ω×(0,T))})$ is sufficiently small, where x₃ is the coordinate along the axis parallel to the cylinder. The time of existence is inversely proportional to I. Existence of solutions is proved by the Leray-Schauder fixed point theorem applied to problems for $h^{(i)} = ∂_{x₃}^{i}v$, $q^{(i)} = ∂_{x₃}^{i}p$, i = 1,2, which follow from the Navier-Stokes equations and corresponding boundary conditions. Existence is proved in Sobolev-Slobodetskiĭ spaces: $h^{(i)} ∈ W_{δ}^{2+β,1+β/2}(Ω×(0,T))$, where i = 1,2, β ∈ (0,1), δ ∈ (1,2), 5/δ < 3 + β, 3/δ < 2 + β.
3
Content available remote

Existence of solutions to the nonstationary Stokes system in $H_{-μ}^{2,1}$, μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

95%
Zajączkowski W.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 2
121-141
EN
We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the second, we show an estimate in 3d in weighted spaces near the axis. Finally, in the third, the existence in a bounded domain is proved. This paper contains the first part of the proof
4
Content available remote

Existence of solutions to the nonstationary Stokes system in $H_{-μ}^{2,1}$, μ ∈ (0,1), in a domain with a distinguished axis. Part 2. Estimate in the 3d case

95%
Zajączkowski W.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 2
143-167
EN
We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v₀ and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (-μ )th power of the distance to the axis. Let $f∈ L_{2,-μ}$, $v₀ ∈ H_{-μ}¹$, μ ∈ (0,1). We prove an estimate of the velocity in the $H_{-μ}^{2,1}$ norm and of the gradient of the pressure in the norm of $L_{2,-μ}$. We apply the Fourier transform with respect to the variable along the axis and the Laplace transform with respect to time. Then we obtain two-dimensional problems with parameters. Deriving an appropriate estimate with a constant independent of the parameters and using estimates in the two-dimensional case yields the result. The existence and regularity in a bounded domain will be shown in another paper.
5
Content available remote

Existence of local solutions for free boundary problems for viscous compressible barotropic fluids

95%
Zajączkowski W.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 3
255-287
EN
We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
6
Content available remote

On stability of axially symmetric solutions to Navier-Stokes equations in a cylindrical domain and with boundary slip conditions

61%
Wiegner M., Zajączkowski W.
Banach Center Publications
|
2005
|
tom 70
|
nr 1
251-278
EN
The existence of global regular axially symmetric solutions to Navier-Stokes equations in a bounded cylinder and for boundary slip conditions is proved. Next, stability of these solutions is shown.
7
Content available remote

Global existence of solutions for incompressible magnetohydrodynamic equations

61%
Alame W., Zajączkowski W.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 2
201-208
EN
Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain Ω ⊂ ℝ³ with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to $W_p^{2,1}(Ω×(0,T))$ and the pressure q satisfies $∇q ∈ L_p(Ω×(0,T))$ for p ≥ 7/3.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.