Long time existence of solutions to 2D Navier-Stokes equations with inflow-outflow and heat convection

Piotr Kacprzyk


Global existence of regular solutions to the Navier-Stokes
equations for velocity and pressure coupled with the heat convection equation
for temperature in cylindrical pipe with inflow and outflow in the
two-dimensional case is shown. We assume the slip boundary conditions for
velocity and the Neumann condition for temperature. First an appropriate
estimate is shown and next the existence of solutions is proved by the
Leray-Schauder fixed point theorem.


Navier-Stokes equations; heat convection; slip boundary condition; Neumann condition; global existence; Leray-Schauder fixed point theorem

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