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Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential
Stagnation-point flow of a rarefied gas impinging obliquely on a plane wall
1. | Department of Mechanical Engineering and Science, and Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto 606-8501, Japan |
2. | School of Engineering Science, Faculty of Engineering, Kyoto University, Kyoto 606-8501, Japan |
References:
[1] |
R. Aris, "Vectors, Tensors, and the Basic Equations of Fluid Mechanics," Chap. 1, Dover, New York, 1989. |
[2] |
J. M. Dorrepaal, An exact solution of the Navier-Stokes equation which describes nonorthogonal stagnation-point flow in two dimensions, J. Fluid Mech., 163 (1986), 141-147.
doi: 10.1017/S0022112086002240. |
[3] |
K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszlynder, Dinglers J., 326 (1911), 321-324, 344-348, 357-362, 372-376, 391-393, 407-410. |
[4] |
J. D. Hoffman, "Numerical Methods for Engineers and Scientists," McGraw-Hill, New York, 1993. |
[5] |
H. W. Liepmann and A. Roshko, "Elements of Gasdynamics. Galcit Aeronautical Series," John Wiley & Sons, Inc., New York, Chapman & Hall, Ltd., London, 1957. |
[6] |
M. J. Martin and I. D. Boyd, Falkner-Skan flow over a wedge with slip boundary conditions, J. Thermophys. Heat Trans., 24 (2010), 263-270. |
[7] |
H. Okamoto, "Mathematical Analysis of the Navier-Stokes Equations," (Japanese) University of Tokyo Press, Tokyo, 2009. |
[8] |
L. Rosenhead, ed., "Laminar Boundary Layers," Clarendon, Oxford, 1966. |
[9] |
Y. Sone, Asymptotic theory of flow of rarefied gas over a smooth boundary I, in"Rarefied Gas Dynamics" (eds. L. Trilling and H. Y. Wachman), Vol. 1, Academic, New York, (1969), 243-253. |
[10] |
Y. Sone, Asymptotic theory of flow of rarefied gas over a smooth boundary II, in "Rarefied Gas Dynamics" (ed. D. Dini), Vol. 2, Editrice Tecnico Scientifica, Pisa, (1971), 737-749. |
[11] |
Y. Sone, Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers, in "Advances in Kinetic Theory and Continuum Mechanics" (eds. R. Gatignol and Soubbaramayer), Springer, Berlin, (1991), 19-31. |
[12] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Birkhäuser, Boston, 2002; Supplementary Notes and Errata: Kyoto University Research Information Repository. Available from: http://hdl.handle.net/2433/66099 . |
[13] |
Y. Sone, "Molecular Gas Dynamics: Theory, Techniques, and Applications," Birkhäuser, Boston, 2007; Supplementary Notes and Errata: Kyoto University Research Information Repository. Available from: http://hdl.handle.net/2433/66098. |
[14] |
Y. Sone and K. Aoki, Steady gas flows past bodies at small Knudsen numbers-Boltzmann and hydrodynamic systems, Transp. Theory Stat. Phys., 16 (1987), 189-199. |
[15] |
J. T. Stuart, The viscous flow near a stagnation point when the external flow has a uniform vorticity, J. Aerosp. Sci., 26 (1959), 124-125. |
[16] |
K. Tamada, Stagnation point flow of rarefied gas, J. Phys. Soc. Jpn., 22 (1967), 1284-1295.
doi: 10.1143/JPSJ.22.1284. |
[17] |
K. Tamada, Two-dimensional stagnation point flow impinging obliquely on a plane wall, J. Phys. Soc. Jpn., 46 (1979), 310-311.
doi: 10.1143/JPSJ.46.310. |
[18] |
C. Y. Wang, Exact solutions of the steady-state Navier-Stokes equations, in "Annu. Rev. Fluid Mech.," Vol. 23, 159-177, Annual Reviews, Palo Alto, CA, 1991. |
[19] |
C. Y. Wang, Stagnation flows with slip: Exact solutions of the Navier-Stokes equations, Z. angew. Math. Phys., 54 (2003), 184-189.
doi: 10.1007/PL00012632. |
[20] |
C. Y. Wang, Similarity stagnation point solutions of the Navier-Stokes equations--review and extension, Eur. J. Mech. B Fluids, 27 (2008), 678-683.
doi: 10.1016/j.euromechflu.2007.11.002. |
show all references
References:
[1] |
R. Aris, "Vectors, Tensors, and the Basic Equations of Fluid Mechanics," Chap. 1, Dover, New York, 1989. |
[2] |
J. M. Dorrepaal, An exact solution of the Navier-Stokes equation which describes nonorthogonal stagnation-point flow in two dimensions, J. Fluid Mech., 163 (1986), 141-147.
doi: 10.1017/S0022112086002240. |
[3] |
K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszlynder, Dinglers J., 326 (1911), 321-324, 344-348, 357-362, 372-376, 391-393, 407-410. |
[4] |
J. D. Hoffman, "Numerical Methods for Engineers and Scientists," McGraw-Hill, New York, 1993. |
[5] |
H. W. Liepmann and A. Roshko, "Elements of Gasdynamics. Galcit Aeronautical Series," John Wiley & Sons, Inc., New York, Chapman & Hall, Ltd., London, 1957. |
[6] |
M. J. Martin and I. D. Boyd, Falkner-Skan flow over a wedge with slip boundary conditions, J. Thermophys. Heat Trans., 24 (2010), 263-270. |
[7] |
H. Okamoto, "Mathematical Analysis of the Navier-Stokes Equations," (Japanese) University of Tokyo Press, Tokyo, 2009. |
[8] |
L. Rosenhead, ed., "Laminar Boundary Layers," Clarendon, Oxford, 1966. |
[9] |
Y. Sone, Asymptotic theory of flow of rarefied gas over a smooth boundary I, in"Rarefied Gas Dynamics" (eds. L. Trilling and H. Y. Wachman), Vol. 1, Academic, New York, (1969), 243-253. |
[10] |
Y. Sone, Asymptotic theory of flow of rarefied gas over a smooth boundary II, in "Rarefied Gas Dynamics" (ed. D. Dini), Vol. 2, Editrice Tecnico Scientifica, Pisa, (1971), 737-749. |
[11] |
Y. Sone, Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers, in "Advances in Kinetic Theory and Continuum Mechanics" (eds. R. Gatignol and Soubbaramayer), Springer, Berlin, (1991), 19-31. |
[12] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Birkhäuser, Boston, 2002; Supplementary Notes and Errata: Kyoto University Research Information Repository. Available from: http://hdl.handle.net/2433/66099 . |
[13] |
Y. Sone, "Molecular Gas Dynamics: Theory, Techniques, and Applications," Birkhäuser, Boston, 2007; Supplementary Notes and Errata: Kyoto University Research Information Repository. Available from: http://hdl.handle.net/2433/66098. |
[14] |
Y. Sone and K. Aoki, Steady gas flows past bodies at small Knudsen numbers-Boltzmann and hydrodynamic systems, Transp. Theory Stat. Phys., 16 (1987), 189-199. |
[15] |
J. T. Stuart, The viscous flow near a stagnation point when the external flow has a uniform vorticity, J. Aerosp. Sci., 26 (1959), 124-125. |
[16] |
K. Tamada, Stagnation point flow of rarefied gas, J. Phys. Soc. Jpn., 22 (1967), 1284-1295.
doi: 10.1143/JPSJ.22.1284. |
[17] |
K. Tamada, Two-dimensional stagnation point flow impinging obliquely on a plane wall, J. Phys. Soc. Jpn., 46 (1979), 310-311.
doi: 10.1143/JPSJ.46.310. |
[18] |
C. Y. Wang, Exact solutions of the steady-state Navier-Stokes equations, in "Annu. Rev. Fluid Mech.," Vol. 23, 159-177, Annual Reviews, Palo Alto, CA, 1991. |
[19] |
C. Y. Wang, Stagnation flows with slip: Exact solutions of the Navier-Stokes equations, Z. angew. Math. Phys., 54 (2003), 184-189.
doi: 10.1007/PL00012632. |
[20] |
C. Y. Wang, Similarity stagnation point solutions of the Navier-Stokes equations--review and extension, Eur. J. Mech. B Fluids, 27 (2008), 678-683.
doi: 10.1016/j.euromechflu.2007.11.002. |
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