Global existence of axially symmetric solutions to Navier-Stokes equations with large angular component of velocity

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

Abstrakty

EN

Global existence of axially symmetric solutions to the Navier-Stokes equations in a cylinder with the axis of symmetry removed is proved. The solutions satisfy the ideal slip conditions on the boundary. We underline that there is no restriction on the angular component of velocity. We obtain two kinds of existence results. First, under assumptions necessary for the existence of weak solutions, we prove that the velocity belongs to $W_{4/3}^{2,1}(Ω × (0,T))$, so it satisfies the Serrin condition. Next, increasing regularity of the external force and initial data we prove existence of solutions (by the Leray-Schauder fixed point theorem) such that $v ∈ W_{r}^{2,1}(Ω × (0,T))$ with r > 4/3, and we prove their uniqueness.

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: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 100
• Numer: 2
• Strony: 243-263

Daty

wydano

2004

Twórcy

autor

Wojciech M. Zajączkowski

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

Identyfikatory

DOI

10.4064/cm100-2-7