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Optimal convergence rates for the compressible NavierStokes equations with potential forces

Renjun Duan Seiji Ukai Tong Yang Huijiang Zhao

Analysis of PDEs mathscidoc:1912.43928

Mathematical Models and Methods in Applied Sciences, 17, (5), 737-758, 2007.5
For the viscous and heat-conductive fluids governed by the compressible NavierStokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the L<sup>p</sup> - L<sup>q</sup> estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L<sup>2</sup>-norm are obtained when the L<sup>1</sup>-norm of the perturbation is bounded.
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@inproceedings{renjun2007optimal,
  title={Optimal convergence rates for the compressible NavierStokes equations with potential forces},
  author={Renjun Duan, Seiji Ukai, Tong Yang, and Huijiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210721003842492},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  volume={17},
  number={5},
  pages={737-758},
  year={2007},
}
Renjun Duan, Seiji Ukai, Tong Yang, and Huijiang Zhao. Optimal convergence rates for the compressible NavierStokes equations with potential forces. 2007. Vol. 17. In Mathematical Models and Methods in Applied Sciences. pp.737-758. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210721003842492.
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