Abstract
The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay ratet −5/4) ast→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.
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Communicated by J. Glimm
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Kawashima, S., Matsumura, A. & Nishida, T. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation. Commun.Math. Phys. 70, 97–124 (1979). https://doi.org/10.1007/BF01982349
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DOI: https://doi.org/10.1007/BF01982349