Long-time behavior of several point particles in a 1D viscous compressible fluid

Abstract

We study the long-time behavior of \textit{several} point particles in a 1D viscous compressible fluid. It is shown that the velocities of the point particles all obey the power law $t^{-3/2}$. This result extends author's previous works on the long-time behavior of a \textit{single} point particle. New difficulties arise in the derivation of pointwise estimates of Green's functions due to infinite reflections of waves in-between the point particles. In particular, the differential equation technique used in previous works alone does not suffice. We overcome this by carefully analyzing the structure of Green's functions in the Laplace variable, especially their asymptotic and analyticity properties.

arXiv comment25 pages

References in corpus (3)

• Long-time behavior for the two-dimensional motion of a disk in a viscous fluid
• Refined pointwise estimates for solutions to the 1D barotropic compressible Navier--Stokes equations: An application to the long-time behavior of a point mass
• Asymptotic analysis of a Neumann problem in a domain with cusp. Application to the collision problem of rigid bodies in a perfect fluid