@article{Chen2024, 
author = {Yangyang Chen and Yixuan Song},
title = {Space-time decay rate of the 3D diffusive and inviscid Oldroyd-B system},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {20271-20303},
keywords = {Oldroyd-B system, diffusive properties, without viscous dissipation, space-time decay rates, weighted Sobolev space},
url = {https://www.sciopen.com/article/10.3934/math.2024987},
doi = {10.3934/math.2024987},
abstract = {We investigate the space-time decay rates of solutions to the 3D Cauchy problem of the compressible Oldroyd-B system with diffusive properties and without viscous dissipation. The main novelties of this paper involve two aspects: On the one hand, we prove that the weighted rate of  k-th order spatial derivative (where  0≤k≤3) of the global solution  (ρ,u,η,τ) is  t−34+k2+γ in the weighted Lebesgue space  Lγ2. On the other hand, we show that the space-time decay rate of the  m-th order spatial derivative (where  m∈[0,2]) of the extra stress tensor of the field in  Lγ2 is  (1+t)−54−m2+γ, which is faster than that of the velocity. The proofs are based on delicate weighted energy methods and interpolation tricks.}
}