Long time existence of solutions to 2d Navier-Stokes equations with heat convection

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

Abstrakty

EN

Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that $v,θ ∈ W_s^{2,1}(Ω^T)$, $∇p ∈ L_s(Ω^T)$, s>2.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 35Q30: 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: 4
• Strony: 453-463

Daty

wydano

2009

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/am36-4-5