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Homogenization and long time asymptotic of a fluid-structure interaction problem

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  • We study the homogenization of an unsteady fluid-structure interaction problem with a scaling corresponding to a long time asymptotic regime. We consider oscillating initial data which are Bloch wave packets corresponding to tubes vibrating in opposition of phase. We prove that the initial displacements follow the rays of geometric optics and that the envelope function evolves according to a Schr ̈odinger equation which can be interpreted as an effect of dispersion.
    Mathematics Subject Classification: Primary: 35B27, 74Q10.


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