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June 2019 Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow
Ruy COIMBRA CHARÃO, Ryo IKEHATA
Hokkaido Math. J. 48(2): 357-383 (June 2019). DOI: 10.14492/hokmj/1562810515

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.

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Ruy COIMBRA CHARÃO. Ryo IKEHATA. "Note on asymptotic profile of solutions to the linearized compressible Navier-Stokes flow." Hokkaido Math. J. 48 (2) 357 - 383, June 2019. https://doi.org/10.14492/hokmj/1562810515

Information

Published: June 2019
First available in Project Euclid: 11 July 2019

zbMATH: 07080100
MathSciNet: MR3980948
Digital Object Identifier: 10.14492/hokmj/1562810515

Subjects:
Primary: 35B40, 35Q30
Secondary: 35C20, 76N99

Rights: Copyright © 2019 Hokkaido University, Department of Mathematics

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Vol.48 • No. 2 • June 2019
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