Math. Model. Nat. Phenom.
Volume 10, Number 3, 2015Model Reduction
|Page(s)||6 - 15|
|Published online||22 June 2015|
The Problem with Hilbert’s 6th Problem
Department of Mathematics, University of Wisconsin, Madison Madison, WI 53706
Corresponding author. E-mail: email@example.com
This paper reviews earlier results of the author regarding the hydrodynamic limit problem for the Boltzmann equation. In particular the key points are that the work of Gorban&Karlin suggests that Korteweg hydrodynamics is implied by the Boltzmann equation and this correspondence is validated by comparison with experimental, analytical, and numerical results. But if the correspondence is indeed valid then passage to limiting compressible Euler equations will not be generally possible after any time for which the the Euler system fails to have smooth solutions.
Dedicated to my friend Alexander Gorban on the occasion of his sixtieth birthday
Mathematics Subject Classification: 35Q20 / 82B40 / 76A02
Key words: Boltzmann equation / hydrodynamic limit / Korteweg hydrodynamics / capillarity / viscosity
© EDP Sciences, 2015
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