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

Yoshiyuki Kagei | Zendy

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

Author(s) -

Yoshiyuki Kagei

Publication year - 2007

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1201012041

Subject(s) - mathematics , semigroup , compressibility , mathematical analysis , mechanics , physics

Asymptotic behavior of solutions to the linearized compressible Navier- Stokes equation around a given constant state is considered in an infi- nite layer Rn−1 × (0,a), n ≥ 2, under the no slip boundary condition for the momentum. The Lp decay estimates of the associated semi- group 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.

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