Global regular solutions to the Navier-Stokes equations in a cylinder

• Autorzy: Wojciech M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to $W_{5/2}^{2,1}(Ω × (0,T))$ and the gradient of the pressure to $L_{5/2}(Ω × (0,T))$. We prove the existence of solutions without any restrictions on the lengths of the initial velocity and the external force.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 76D05: Navier-Stokes equations
• 35K20: Initial-boundary value problems for second-order parabolic equations
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 74
• Numer: 1
• Strony: 235-255

Daty

wydano

2006

Twórcy

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, S. Kaliskiego 2, 00-908 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc74-0-15