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Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle

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Abstract

Given an obstacle in \({\mathbb{R}^3}\) and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as \({|x|\to \infty}\), which approaches the corresponding Navier–Stokes steady flow, as the mean-free path goes to zero. Furthermore, we establish the error estimate between the Boltzmann solution and its Navier–Stokes approximation. Our method consists of new L6 and L3 estimates in the unbounded exterior domain, as well as an iterative scheme preserving the positivity of the distribution function.

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Authors and Affiliations

  1. International Research Center M&MOCS, Univ. dell’Aquila, 04012, Cisterna di Latina, LT, Italy

    R. Esposito

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02812, USA

    Y. Guo

  3. Dipartimento di Fisica and Unità INFN, Università di Roma Tor Vergata, 00133, Rome, Italy

    R. Marra

Authors
  1. R. Esposito
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  2. Y. Guo
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  3. R. Marra
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Correspondence to R. Esposito.

Additional information

Communicated by H. Spohn

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Esposito, R., Guo, Y. & Marra, R. Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle. Commun. Math. Phys. 364, 765–823 (2018). https://doi.org/10.1007/s00220-018-3173-1

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  • DOI: https://doi.org/10.1007/s00220-018-3173-1

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