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

W. M. Zajączkowski. "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." Applicationes Mathematicae 34.2 (2007): 121-141. <http://eudml.org/doc/279225>.

@article{W2007,
abstract = {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},
author = {W. M. Zajączkowski},
journal = {Applicationes Mathematicae},
language = {eng},
number = {2},
pages = {121-141},
title = {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},
url = {http://eudml.org/doc/279225},
volume = {34},
year = {2007},
}

TY - JOUR
AU - W. M. Zajączkowski
TI - 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
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 2
SP - 121
EP - 141
AB - 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
LA - eng
UR - http://eudml.org/doc/279225
ER -