Some spatial decay estimates in time-dependent stokes slow flows

Abstract

This paper uses a time-weighted cross-sectional area measure in order to establish spatial decay estimates for the time-dependent Stokes slow flow of an incompressible viscous fluid in a semi- infinite cylindrical pipe of smooth cross section. The decay rate predicted in this paper depends only on the constant kinematic viscosity and the smallest positive eigenvalue of the free membrane problem as well as two geometric characteristics of the cross section of the pipe.

Keywords:

• Stokes flow
• decay estimates
• time-weighted measure

AMS:

• 35Q30
• 35B45
• 76D07