Global regular nonstationary flow for the Navier–Stokes equations in a cylindrical pipe

Piotr Kacprzyk¹

¹ Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland

Applicationes Mathematicae, Tome 34 (2007) no. 3, pp. 289-307.

Résumé

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. Global existence is proved in two steps. First, by the Leray–Schauder fixed point theorem we prove local existence with large existence time. Next, the local solution is prolonged step by step. The existence is proved without any restrictions on the magnitudes of the inflow, outflow, external force and initial velocity.

Détail

DOI : 10.4064/am34-3-3

Keywords: global existence regular solutions navier stokes equations describing motion incompressible viscous fluid cylindrical pipe large inflow outflow shown global existence proved steps first leray schauder fixed point theorem prove local existence large existence time local solution prolonged step step existence proved without restrictions magnitudes inflow outflow external force initial velocity