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

• Autorzy: Piotr Kacprzyk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 76D05: Navier-Stokes equations
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2009
• Tom: 36
• Numer: 2
• Strony: 195-212

Daty

wydano

2009

Twórcy

autor

Piotr Kacprzyk

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

Identyfikatory

DOI

10.4064/am36-2-7