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The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth
Boltzmann equation and hydrodynamics at the Burnett level
1. | Department of Mathematics, Karlstad University, SE-651 88 Karlstad |
References:
[1] |
M. Bisi, M. P. Cassinari and M. Groppi, Qualitative analysis of the generalized Burnett equations and applications to half-space problems, Kinet. Relat. Models, 1 (2008), 295-312.
doi: 10.3934/krm.2008.1.295. |
[2] |
A. V. Bobylev, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Sov. Phys. Dokl., 27 (1982), 29-31. |
[3] |
A. V. Bobylev, Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations, J. Stat. Phys., 124 (2006), 371-399.
doi: 10.1007/s10955-005-8087-6. |
[4] |
A. V. Bobylev, Generalized Burnett hydrodynamics, J. Stat. Phys., 132 (2008), 569-580. |
[5] |
A. V. Bobylev, M. Bisi, M. P. Cassinari and G. Spiga, Shock wave structure for generalized Burnett equations, Phys. of Fluids, 23 (2011). |
[6] |
D. Burnett, The distribution of velocities in a slightly non-uniform gas, Proc. London. Math. Soc., 39 (1935), 385-430.
doi: 10.1112/plms/s2-39.1.385. |
[7] |
D. Burnett, The distribution of molecular velocities and the mean motion in a non-uniform gas, Proc. London. Math. Soc., 40 (1935), 382-435.
doi: 10.1112/plms/s2-40.1.382. |
[8] |
C. Cercignani, "The Boltzmann Equation and its Applications,'' Springer-Verlag, 1988. |
[9] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases," Cambrige University Press, 1990. |
[10] |
J. H. Ferziger and H. G. Kaper, "Mathematical Theory of Transport Processes in Gases," North-Holland, 1972. |
[11] |
S. Jin and M. Slemrod, Regularization of the Burnett equations via relaxation, J. Stat. Phys., 103 (2001), 1009-1033.
doi: 10.1023/A:1010365123288. |
[12] | |
[13] |
M. M. Postnikov, "Stable Polynomials," Nauka, Moscow, 1981 (in Russian). |
[14] |
M. Slemrod, A normalization method for the Chapman-Enskog expansion, Physica D, 109 (1997), 257-273.
doi: 10.1016/S0167-2789(97)00068-7. |
[15] |
M. Slemrod, Constitutive relations for monoatomic gases based on a generalized rational approximation to the sum of the Chapman-Enskog expansion, Arch. Rat. Mech. Anal, 150 (1999), 1-22.
doi: 10.1007/s002050050178. |
[16] |
M. Slemrod, In the Chapman-Enskog expansion the Burnett coefficients satisfy the universal relation $\omega_3+\omega_4+\theta_3=0$, Arch. Rat. Mech. Anal., 161 (2002), 339-344.
doi: 10.1007/s002050100180. |
[17] |
M. Torrilon and H. Struchtrup, Regularized 13 moment equations: Shock structure calculations and comparison to Burnett models, J. Fluid Mech., 513 (2004), 171-198.
doi: 10.1017/S0022112004009917. |
[18] |
C. Truesdell and R. G. Muncaster, "Fundamental of Maxwell's Kinetic Theory of a Simple Monoatomic Gas," Academic Press, New York, 1980. |
show all references
References:
[1] |
M. Bisi, M. P. Cassinari and M. Groppi, Qualitative analysis of the generalized Burnett equations and applications to half-space problems, Kinet. Relat. Models, 1 (2008), 295-312.
doi: 10.3934/krm.2008.1.295. |
[2] |
A. V. Bobylev, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Sov. Phys. Dokl., 27 (1982), 29-31. |
[3] |
A. V. Bobylev, Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations, J. Stat. Phys., 124 (2006), 371-399.
doi: 10.1007/s10955-005-8087-6. |
[4] |
A. V. Bobylev, Generalized Burnett hydrodynamics, J. Stat. Phys., 132 (2008), 569-580. |
[5] |
A. V. Bobylev, M. Bisi, M. P. Cassinari and G. Spiga, Shock wave structure for generalized Burnett equations, Phys. of Fluids, 23 (2011). |
[6] |
D. Burnett, The distribution of velocities in a slightly non-uniform gas, Proc. London. Math. Soc., 39 (1935), 385-430.
doi: 10.1112/plms/s2-39.1.385. |
[7] |
D. Burnett, The distribution of molecular velocities and the mean motion in a non-uniform gas, Proc. London. Math. Soc., 40 (1935), 382-435.
doi: 10.1112/plms/s2-40.1.382. |
[8] |
C. Cercignani, "The Boltzmann Equation and its Applications,'' Springer-Verlag, 1988. |
[9] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases," Cambrige University Press, 1990. |
[10] |
J. H. Ferziger and H. G. Kaper, "Mathematical Theory of Transport Processes in Gases," North-Holland, 1972. |
[11] |
S. Jin and M. Slemrod, Regularization of the Burnett equations via relaxation, J. Stat. Phys., 103 (2001), 1009-1033.
doi: 10.1023/A:1010365123288. |
[12] | |
[13] |
M. M. Postnikov, "Stable Polynomials," Nauka, Moscow, 1981 (in Russian). |
[14] |
M. Slemrod, A normalization method for the Chapman-Enskog expansion, Physica D, 109 (1997), 257-273.
doi: 10.1016/S0167-2789(97)00068-7. |
[15] |
M. Slemrod, Constitutive relations for monoatomic gases based on a generalized rational approximation to the sum of the Chapman-Enskog expansion, Arch. Rat. Mech. Anal, 150 (1999), 1-22.
doi: 10.1007/s002050050178. |
[16] |
M. Slemrod, In the Chapman-Enskog expansion the Burnett coefficients satisfy the universal relation $\omega_3+\omega_4+\theta_3=0$, Arch. Rat. Mech. Anal., 161 (2002), 339-344.
doi: 10.1007/s002050100180. |
[17] |
M. Torrilon and H. Struchtrup, Regularized 13 moment equations: Shock structure calculations and comparison to Burnett models, J. Fluid Mech., 513 (2004), 171-198.
doi: 10.1017/S0022112004009917. |
[18] |
C. Truesdell and R. G. Muncaster, "Fundamental of Maxwell's Kinetic Theory of a Simple Monoatomic Gas," Academic Press, New York, 1980. |
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