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Séminaire de EDP - Physique Mathématique

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

Kai Koike

( Tokyo Tech )

Salle de conférences

le 12 mars 2024 à 11:00

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 X(t)X(t) satisfies a decay estimate X(t)=O(t3/2+ϵ)X(t)=O(t^{-3/2+\epsilon}) for any ϵ>0\epsilon>0. This result is obtained as an application of pointwise estimates of solutions obtained through the use of Green’s function.