On the C₀ semigroup generated by the Oseen operator around a steady flow exterior to a rotating obstacle

2020/03/16 by Jingyue Li, Changxing Miao, Li, Jingyue +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.07026

Abstract

We consider the motion of an incompressible viscous fluid filling the whole space exterior to a moving with rotation and translation obstacle. We show that the Stokes operator around the steady flow in the exterior of this obstacle generates a C₀-semigroup in L^p space and then develop a series of L^p-L^q estimates of such semigroup. As an application, we give out the stability of such steady flow when the initial disturbance in L³ and the steady flow are sufficiently small.

Citations

• L q -L r estimates for solutions of the nonstationary stokes equations in an exterior domain and the Navier-Stokes initial value problems inL q spaces
• L p -L q Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle
• On the Oseen equation in the three dimensional exterior domains

Related

• The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The\n non-autonomous case
• Nonlinear spectral instability of steady-state flow of a viscous liquid past a rotating obstacle
• Navier--Stokes flow in the exterior of a moving obstacle with a Lipschitz boundary
• On the large time L^∞-estimates of the Stokes semigroup in two-dimensional exterior domains
• Anisotropically weighted L^q-L^r estimates of the Oseen semigroup in exterior domains, with applications to the Navier-Stokes flow past a rigid body