On global regular solutions to the Navier-Stokes equations with heat convection

• Autorzy: Piotr Kacprzyk
• Języki publikacji: EN

Abstrakty

EN

Global existence of regular solutions to the Navier-Stokes equations for velocity and pressure coupled with the heat convection equation for temperature in a cylindrical pipe is shown. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First we prove long time existence of regular solutions in [kT,(k+1)T]. Having T sufficiently large and imposing some decay estimates on $||f(t)||_{L₂(Ω)}$, $||f_{,x₃}(t)||_{L₂(Ω)}$ we continue the local solutions step by step up to a global one.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 108
• Numer: 2
• Strony: 155-184

Daty

wydano

2013

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/ap108-2-3