JournalsprimsVol. 43, No. 3pp. 763–794

Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Infinite Layer

  • Yoshiyuki Kagei

    Kyushu University, Fukuoka, Japan
Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Infinite Layer cover
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Abstract

Asymptotic behavior of solutions to the linearized compressible Navier–Stokes equation around a given constant state is considered in an infinite layer ℝ_n_−1 × (0, a), n ≥ 2, under the no slip boundary condition for the momentum. The L__p decay estimates of the associated semigroup are established for all 1 ≤ p ≤ ∞. It is also shown that the time-asymptotic leading part of the semigroup is given by an n − 1 dimensional heat semigroup.

Cite this article

Yoshiyuki Kagei, Asymptotic Behavior of the Semigroup Associated with the Linearized Compressible Navier–Stokes Equation in an Infinite Layer. Publ. Res. Inst. Math. Sci. 43 (2007), no. 3, pp. 763–794

DOI 10.2977/PRIMS/1201012041