Geodesic
From the Boltzmann Equation to Hydrodynamic Equations in thin Layers
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 163-186

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The present paper discusses an asymptotic theory for the Boltzmann equation leading to either the Prandtl incompressible boundary layer equations, or the incompressible hydrostatic equations. These results are formal, and based on the same moment method used in [C. Bardos, F. Golse, D. Levermore, J. Stat. Phys 63 (1991), pp. 323-344] to derive the incompressible Euler and Navier-Stokes equations from the Boltzmann equation. 
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     author = {Golse, Fran\c{c}ois},
     title = {From the {Boltzmann} {Equation} to {Hydrodynamic} {Equations} in thin {Layers}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {163--186},
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     volume = {Ser. 9, 4},
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     year = {2011},
     zbl = {1235.35208},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a0/}
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Golse, François. From the Boltzmann Equation to Hydrodynamic Equations in thin Layers. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 163-186. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a0/