Global regular solutions to the Navier-Stokes equations in an axially symmetric domain
Keywords
Navier-Stokes equations, axially symmetric domain, global regular solutions, slip boundary conditionsAbstract
We prove the existence of global regular solutions to the Navier-Stokes equations in an axially symmetric domain in $\mathbb R^3$ and with boundary slip conditions. We assume that initial angular component of velocity and 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. 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 $T$.Downloads
Published
2009-06-01
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ZAJĄCZKOWSKI, Wojciech M. Global regular solutions to the Navier-Stokes equations in an axially symmetric domain. Topological Methods in Nonlinear Analysis. Online. 1 June 2009. Vol. 33, no. 2, pp. 233 - 274. [Accessed 24 April 2024].
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