@article{Ye2023, 
author = {Qin Ye},
title = {Space-time decay rate of high-order spatial derivative of solution for 3D compressible Euler equations with damping},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {7},
pages = {3879-3894},
keywords = {compressible Euler equations, space-time decay rate, weighted estimate},
url = {https://www.sciopen.com/article/10.3934/era.2023197},
doi = {10.3934/era.2023197},
abstract = {We are concerned with the space-time decay rate of high-order spatial derivatives of solutions for 3D compressible Euler equations with damping. For any integer    ℓ  ≥  3, Kim (2022) showed the space-time decay rate of the    k  (  0  ≤  k  ≤  ℓ  −  2  )th-order spatial derivative of the solution. By making full use of the structure of the system, and employing different weighted energy methods for    0  ≤  k  ≤  ℓ  −  2  ,  k  =  ℓ  −  1  ,  k  =  ℓ, it is shown that the space-time decay rate of the    (  ℓ  −  1  )th-order and    ℓth-order spatial derivative of the strong solution in weighted Lebesgue space        L    σ    2   are        t          −              3        4            −                        ℓ          −          1                2            +              σ        2             and        t          −              3        4            −              ℓ        2            +              σ        2             respectively, which are totally new as compared to that of Kim (2022) [1].}
}