# Global regular solutions to the Navier-Stokes equations in a cylinder

Banach Center Publications (2006)

- Volume: 74, Issue: 1, page 235-255
- ISSN: 0137-6934

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topWojciech M. Zajączkowski. "Global regular solutions to the Navier-Stokes equations in a cylinder." Banach Center Publications 74.1 (2006): 235-255. <http://eudml.org/doc/282116>.

@article{WojciechM2006,

abstract = {The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to $W_\{5/2\}^\{2,1\}(Ω × (0,T))$ and the gradient of the pressure to $L_\{5/2\}(Ω × (0,T))$. We prove the existence of solutions without any restrictions on the lengths of the initial velocity and the external force.},

author = {Wojciech M. Zajączkowski},

journal = {Banach Center Publications},

keywords = {axial symmetry; existence; large initial velocity; external force},

language = {eng},

number = {1},

pages = {235-255},

title = {Global regular solutions to the Navier-Stokes equations in a cylinder},

url = {http://eudml.org/doc/282116},

volume = {74},

year = {2006},

}

TY - JOUR

AU - Wojciech M. Zajączkowski

TI - Global regular solutions to the Navier-Stokes equations in a cylinder

JO - Banach Center Publications

PY - 2006

VL - 74

IS - 1

SP - 235

EP - 255

AB - The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to $W_{5/2}^{2,1}(Ω × (0,T))$ and the gradient of the pressure to $L_{5/2}(Ω × (0,T))$. We prove the existence of solutions without any restrictions on the lengths of the initial velocity and the external force.

LA - eng

KW - axial symmetry; existence; large initial velocity; external force

UR - http://eudml.org/doc/282116

ER -

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