The Optimal Decay Estimates on the Framework of Besov Spaces for Generally Dissipative Systems

研究成果: Article

16 引用 (Scopus)

抄録

We give a new decay framework for the general dissipative hyperbolic system and the hyperbolic–parabolic composite system, which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts. New ingredients lie in the high-frequency and low-frequency decomposition of a pseudo-differential operator and an interpolation inequality related to homogeneous Besov spaces of negative order. Furthermore, we develop the Littlewood–Paley pointwise energy estimates and new time-weighted energy functionals to establish optimal decay estimates on the framework of spatially critical Besov spaces for the degenerately dissipative hyperbolic system of balance laws. Based on the Lp(ℝn) embedding and the improved Gagliardo–Nirenberg inequality, the optimal Lp(ℝn)-L2(ℝn)(1 ≦ p < 2) decay rates and Lp(ℝn)-Lq(ℝn)(1 ≦ p < 2 ≦ q ≦ ∞) decay rates are further shown. Finally, as a direct application, the optimal decay rates for three dimensional damped compressible Euler equations are also obtained.

元の言語English
ページ(範囲)275-315
ページ数41
ジャーナルArchive for Rational Mechanics and Analysis
218
発行部数1
DOI
出版物ステータスPublished - 2015 10 27
外部発表Yes

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Decay Estimates
Dissipative Systems
Euler equations
Besov Spaces
Decay Rate
Spectrum analysis
Mathematical operators
Large scale systems
Interpolation
Hyperbolic Systems
Decomposition
Interpolation Inequality
Compressible Euler Equations
Balance Laws
Pointwise Estimates
Energy Estimates
Pseudodifferential Operators
Homogeneous Space
Spectral Analysis
Damped

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

これを引用

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abstract = "We give a new decay framework for the general dissipative hyperbolic system and the hyperbolic–parabolic composite system, which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts. New ingredients lie in the high-frequency and low-frequency decomposition of a pseudo-differential operator and an interpolation inequality related to homogeneous Besov spaces of negative order. Furthermore, we develop the Littlewood–Paley pointwise energy estimates and new time-weighted energy functionals to establish optimal decay estimates on the framework of spatially critical Besov spaces for the degenerately dissipative hyperbolic system of balance laws. Based on the Lp(ℝn) embedding and the improved Gagliardo–Nirenberg inequality, the optimal Lp(ℝn)-L2(ℝn)(1 ≦ p < 2) decay rates and Lp(ℝn)-Lq(ℝn)(1 ≦ p < 2 ≦ q ≦ ∞) decay rates are further shown. Finally, as a direct application, the optimal decay rates for three dimensional damped compressible Euler equations are also obtained.",
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N2 - We give a new decay framework for the general dissipative hyperbolic system and the hyperbolic–parabolic composite system, which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts. New ingredients lie in the high-frequency and low-frequency decomposition of a pseudo-differential operator and an interpolation inequality related to homogeneous Besov spaces of negative order. Furthermore, we develop the Littlewood–Paley pointwise energy estimates and new time-weighted energy functionals to establish optimal decay estimates on the framework of spatially critical Besov spaces for the degenerately dissipative hyperbolic system of balance laws. Based on the Lp(ℝn) embedding and the improved Gagliardo–Nirenberg inequality, the optimal Lp(ℝn)-L2(ℝn)(1 ≦ p < 2) decay rates and Lp(ℝn)-Lq(ℝn)(1 ≦ p < 2 ≦ q ≦ ∞) decay rates are further shown. Finally, as a direct application, the optimal decay rates for three dimensional damped compressible Euler equations are also obtained.

AB - We give a new decay framework for the general dissipative hyperbolic system and the hyperbolic–parabolic composite system, which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts. New ingredients lie in the high-frequency and low-frequency decomposition of a pseudo-differential operator and an interpolation inequality related to homogeneous Besov spaces of negative order. Furthermore, we develop the Littlewood–Paley pointwise energy estimates and new time-weighted energy functionals to establish optimal decay estimates on the framework of spatially critical Besov spaces for the degenerately dissipative hyperbolic system of balance laws. Based on the Lp(ℝn) embedding and the improved Gagliardo–Nirenberg inequality, the optimal Lp(ℝn)-L2(ℝn)(1 ≦ p < 2) decay rates and Lp(ℝn)-Lq(ℝn)(1 ≦ p < 2 ≦ q ≦ ∞) decay rates are further shown. Finally, as a direct application, the optimal decay rates for three dimensional damped compressible Euler equations are also obtained.

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