Kai Koike (Tokyo Institute of Technology)

Long-time behavior of a harmonic oscillator in a 1D viscous compressible fluid.

We study the long-time behavior of a harmonic oscillator in a 1D viscous compressible fluid. It is shown that the displacement of the oscillator satisfies a decay estimate $O(t^{-3/2+\epsilon})$ for any $\epsilon>0$. This result is obtained as an application of a pointwise asymptotic expansion of the flow through the use of Green’s function.