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January  2011, 15(1): 137-170. doi: 10.3934/dcdsb.2011.15.137

The initial layer for Rayleigh problem

Hung-Wen Kuo 1,

1. 

Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

Received  August 2009 Revised  July 2010 Published  October 2010

Rayleigh's problem of an infinite flat plate set into uniform motion impulsively in its own plane is studied by using the BKW model, the linearized Boltzmann equation and the full Boltzmann equation, respectively. The purpose is to study the gas motion under the diffuse reflection boundary condition. For a small impulsive velocity (small Mach number) and short time, the flow behaves like a free molecule flow. Our analysis is based on certain pointwise estimates for the solution of the problem and flow velocity.
Keywords: Boltzmann equation, initial layer., Rayleigh problem.
Mathematics Subject Classification: Primary: 76P05; Secondary: 45K05, 82C4.
Citation: Hung-Wen Kuo. The initial layer for Rayleigh problem. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 137-170. doi: 10.3934/dcdsb.2011.15.137
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E. P. Gross and E. A. Jackson, Kinetic theory of the impulsive motion of an infinite plane,, Phys. Fluids, 1 (1958), 318. doi: doi:10.1063/1.1705890. Google Scholar

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Y. Sone, Kinetic theory analysis of the linearized Rayleigh problem,, Phys. Fluids, 7 (1964), 470. doi: doi:10.1063/1.1711221. Google Scholar

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Y. Sone, "Kinetic Theory and Fluid Dynamics,", Modeling and Simulation in Science, (2002). Google Scholar

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Y. Sone, "Molecular Gas Dynamics. Theory, Techniques, and Applications,", Modeling and Simulation in Science, (2007). Google Scholar

show all references

References:
[1]

C. Cercignani, R. Illner and M. Pulvirenti, "The Mathematical Theory of Dilute Gases,", Applied Mathematical Sciences, 106 (1994). Google Scholar

[2]

E. P. Gross and E. A. Jackson, Kinetic theory of the impulsive motion of an infinite plane,, Phys. Fluids, 1 (1958), 318. doi: doi:10.1063/1.1705890. Google Scholar

[3]

Hsun-Tiao Yang and Lester. Lees, Rayleigh's problem at low Mach number according to the kinetic theory of gases,, J. Math. and Phys, 35 (1956), 192. Google Scholar

[4]

Y. Sone, Kinetic theory analysis of the linearized Rayleigh problem,, Phys. Fluids, 7 (1964), 470. doi: doi:10.1063/1.1711221. Google Scholar

[5]

Y. Sone, "Kinetic Theory and Fluid Dynamics,", Modeling and Simulation in Science, (2002). Google Scholar

[6]

Y. Sone, "Molecular Gas Dynamics. Theory, Techniques, and Applications,", Modeling and Simulation in Science, (2007). Google Scholar

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