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June 2009 Large time existence of solutions to the Navier-Stokes equations in axially symmetric domains with inflow and outflow
Wojciech M. Zajączkowski
Funct. Approx. Comment. Math. 40(2): 209-250 (June 2009). DOI: 10.7169/facm/1246454029

Abstract

We prove a long time existence of special regular solutions to the Navier-Stokes equations in an axially symmetric domain in $\mathbb{R}^3$, with boundary slip conditions and with inflow and outflow. We assume that an initial angular component of velocity and an angular component of the external force and angular derivatives of the cylindrical components of initial velocity and of the external force are sufficiently small in corresponding norms. We assume also that inflow and outflow is sufficiently close to homogeneous. Then there exists a solution such that velocity belongs to $W_{5/2}^{2,1}(\Omega^T)$ and gradient of pressure to $L_{5/2}(\Omega^T)$, and we do not have restrictions on~$T$.

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Wojciech M. Zajączkowski. "Large time existence of solutions to the Navier-Stokes equations in axially symmetric domains with inflow and outflow." Funct. Approx. Comment. Math. 40 (2) 209 - 250, June 2009. https://doi.org/10.7169/facm/1246454029

Information

Published: June 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1187.35161
MathSciNet: MR2543557
Digital Object Identifier: 10.7169/facm/1246454029

Subjects:
Primary: 35Q35
Secondary: 35K20, 76D03, 76D05

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.40 • No. 2 • June 2009
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