Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

Yoshiyuki Kagei; Shuichi Kawashima

doi:10.1007/s00220-006-0017-1

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

Yoshiyuki Kagei^*, Shuichi Kawashima

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

57 Citations (Scopus)

Abstract

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ₊ⁿ (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in H^s (ℝ₊ⁿ) s ≥ [n/2]+1 and the perturbations decay in L ^∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

Original language	English
Pages (from-to)	401-430
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	266
Issue number	2
DOIs	https://doi.org/10.1007/s00220-006-0017-1
Publication status	Published - 2006 Sept 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-006-0017-1

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abstract = "Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+n) s ≥ [n/2]+1 and the perturbations decay in L ∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.",

author = "Yoshiyuki Kagei and Shuichi Kawashima",

year = "2006",

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doi = "10.1007/s00220-006-0017-1",

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AU - Kagei, Yoshiyuki

AU - Kawashima, Shuichi

PY - 2006/9/1

Y1 - 2006/9/1

N2 - Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+n) s ≥ [n/2]+1 and the perturbations decay in L ∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

AB - Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space ℝ+n (n ≥ 2)$$ under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in Hs (ℝ+n) s ≥ [n/2]+1 and the perturbations decay in L ∞ norm as t →∞, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

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Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

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