### Abstract

Decay estimates on solutions to the linearized compressible NavierStokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L ^{2} norm as an (n - 1)-dimensional heat kernel. Furthermore, it is proved that the asymptotic leading part of solutions is given by solutions of an (n - 1)-dimensional linear heat equation with a convective term multiplied by time-periodic function.

Original language | English |
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Article number | 1250007 |

Journal | Mathematical Models and Methods in Applied Sciences |

Volume | 22 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Applied Mathematics

### Cite this

**Decay properties of solutions to the linearized compressible navierstokes equation around time-periodic parallel flow.** / Brezina, Jan; Kagei, Yoshiyuki.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Decay properties of solutions to the linearized compressible navierstokes equation around time-periodic parallel flow

AU - Brezina, Jan

AU - Kagei, Yoshiyuki

PY - 2012/7/1

Y1 - 2012/7/1

N2 - Decay estimates on solutions to the linearized compressible NavierStokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L 2 norm as an (n - 1)-dimensional heat kernel. Furthermore, it is proved that the asymptotic leading part of solutions is given by solutions of an (n - 1)-dimensional linear heat equation with a convective term multiplied by time-periodic function.

AB - Decay estimates on solutions to the linearized compressible NavierStokes equation around time-periodic parallel flow are established. It is shown that if the Reynolds and Mach numbers are sufficiently small, solutions of the linearized problem decay in L 2 norm as an (n - 1)-dimensional heat kernel. Furthermore, it is proved that the asymptotic leading part of solutions is given by solutions of an (n - 1)-dimensional linear heat equation with a convective term multiplied by time-periodic function.

UR - http://www.scopus.com/inward/record.url?scp=84860362555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860362555&partnerID=8YFLogxK

U2 - 10.1142/S0218202512500078

DO - 10.1142/S0218202512500078

M3 - Article

VL - 22

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 7

M1 - 1250007

ER -