Hokkaido Mathematical Journal

Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow

Ruy COIMBRA CHARÃO and Ryo IKEHATA

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Abstract

We consider the asymptotic behavior as $t \to +\infty$ of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the decay rate for the $L^{2}$-norm of the velocity by deriving a decay estimate from below as $t \to +\infty$. To get the estimates in the zone of high frequency we use a version of the energy method in the Fourier space combined with the Haraux-Komornik inequality and this seems much different from known techniques to study compressible Navier-Stokes system.

Article information

Source
Hokkaido Math. J., Volume 48, Number 2 (2019), 357-383.

Dates
First available in Project Euclid: 11 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1562810515

Digital Object Identifier
doi:10.14492/hokmj/1562810515

Mathematical Reviews number (MathSciNet)
MR3980948

Zentralblatt MATH identifier
07080100

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35B40: Asymptotic behavior of solutions
Secondary: 76N99: None of the above, but in this section 35C20: Asymptotic expansions

Keywords
Compressible Navier-Stokes equations Cauchy problem Asymptotic profiles Weighted $L^{1}$-initial data Low and high frequencies

Citation

COIMBRA CHARÃO, Ruy; IKEHATA, Ryo. Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow. Hokkaido Math. J. 48 (2019), no. 2, 357--383. doi:10.14492/hokmj/1562810515. https://projecteuclid.org/euclid.hokmj/1562810515


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