Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder

Piotr Kacprzyk. "Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder." Applicationes Mathematicae 36.2 (2009): 195-212. <http://eudml.org/doc/280010>.

@article{PiotrKacprzyk2009,
abstract = {Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary and with respect to time in some norms. The global existence is proved step by step using the existence on the time interval [0,T], with T sufficiently large.},
author = {Piotr Kacprzyk},
journal = {Applicationes Mathematicae},
keywords = {Navier–Stokes equations; inflow-outflow problem; slip boundary conditions; cylindrical domains; global existence of regular solutions},
language = {eng},
number = {2},
pages = {195-212},
title = {Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder},
url = {http://eudml.org/doc/280010},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Piotr Kacprzyk
TI - Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 2
SP - 195
EP - 212
AB - Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary and with respect to time in some norms. The global existence is proved step by step using the existence on the time interval [0,T], with T sufficiently large.
LA - eng
KW - Navier–Stokes equations; inflow-outflow problem; slip boundary conditions; cylindrical domains; global existence of regular solutions
UR - http://eudml.org/doc/280010
ER -