Long time existence of regular solutions to 3d Navier-Stokes equations coupled with heat convection

• Autorzy: Jolanta Socała , Wojciech M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

We prove long time existence of regular solutions to the Navier-Stokes equations coupled with the heat equation. We consider the system in a non-axially symmetric cylinder, with the slip boundary conditions for the Navier-Stokes equations, and the Neumann condition for the heat equation. The long time existence is possible because the derivatives, with respect to the variable along the axis of the cylinder, of the initial velocity, initial temperature and external force are assumed to be sufficiently small in the L₂ norms. We prove the existence of solutions such that the velocity and temperature belong to $W_σ^{2,1}(Ω × (0,T))$, where σ > 5/3. The existence is proved by using the Leray-Schauder fixed point theorem.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 35K05: Heat equation
• 76D05: Navier-Stokes equations
• 35K20: Initial-boundary value problems for second-order parabolic equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2012
• Tom: 39
• Numer: 2
• Strony: 231-242

Daty

wydano

2012

Twórcy

autor

Jolanta Socała

• State Higher Vocational School in Racibórz, Słowacki St. 55, 47-400 Racibórz, Poland

autor

Wojciech M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
• Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

Identyfikatory

DOI

10.4064/am39-2-8