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Lp convergence rates of planar waves for multi-dimensional Euler equations with damping

Jie Liao Weike Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43969

Journal of Differential Equations, 247, (1), 303-329, 2009.7
In this paper, the L p convergence rates of planar diffusion waves for multi-dimensional Euler equations with damping are considered. The analysis relies on a newly introduced frequency decomposition and Green function based energy method. It is a combination of the L p estimate on the low frequency component by using an approximate Green function and L 2 estimate on the high frequency component through the energy method. By noticing that the low frequency component in the approximate Green function has the algebraic decay which governs the large time behavior, while the high frequency component has the exponential decay but with singularity, their combination leads to a global algebraic decay estimate. To use the decay property only of the low frequency component in the approximate Green function avoids the singularity in the high frequency component so that it simplifies and improves the
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@inproceedings{jie2009lp,
  title={Lp convergence rates of planar waves for multi-dimensional Euler equations with damping},
  author={Jie Liao, Weike Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210956608729533},
  booktitle={Journal of Differential Equations},
  volume={247},
  number={1},
  pages={303-329},
  year={2009},
}
Jie Liao, Weike Wang, and Tong Yang. Lp convergence rates of planar waves for multi-dimensional Euler equations with damping. 2009. Vol. 247. In Journal of Differential Equations. pp.303-329. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210956608729533.
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