At the present time, the incompressible Navier-Stokes limit is the only hydrodynamic asymptotics of the Boltzmann equation for which an optimal convergence result is known (and for which we are actually able to implement all the mathematical tools presented in the previous chapter). By “optimal”, we mean here that this convergence result
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holds globally in time;
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does not require any assumption on the initial velocity profle
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does not assume any constraint on the initial thermodynamic fields;
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takes into account boundary conditions, and describes their limiting form.
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© 2009 Springer-Verlag Berlin Heidelberg
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Saint-Raymond, L. (2009). The incompressible Navier-Stokes limit. In: Hydrodynamic Limits of the Boltzmann Equation. Lecture Notes in Mathematics(), vol 1971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92847-8_4
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DOI: https://doi.org/10.1007/978-3-540-92847-8_4
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