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Asymptotic Behavior of the Linearized Semigroup at Space-Periodic Stationary Solution of the Compressible Navier–Stokes Equation

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Abstract

The asymptotic behavior of the linearized semigroup at spatially periodic stationary solution of the compressible Navier–Stokes equation in a periodic layer of \(\mathbb {R}^n\) \((n=2,3)\) is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the linearized semigroup is decomposed into two parts; one behaves like a solution of an \(n-1\) dimensional linear heat equation as time goes to infinity and the other one decays exponentially.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Nishi-ku, Motooka 744, Fukuoka, 819-0395, Japan

    Shota Enomoto

  2. Faculty of Mathematics, Kyushu University, Nishi-ku, Motooka 744, Fukuoka, 819-0395, Japan

    Yoshiyuki Kagei

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  1. Shota Enomoto
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  2. Yoshiyuki Kagei
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Correspondence to Yoshiyuki Kagei.

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Communicated by Y. Shibata.

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Enomoto, S., Kagei, Y. Asymptotic Behavior of the Linearized Semigroup at Space-Periodic Stationary Solution of the Compressible Navier–Stokes Equation. J. Math. Fluid Mech. 19, 739–772 (2017). https://doi.org/10.1007/s00021-016-0304-3

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