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On the homogeneous Boltzmann equation with soft-potential collision kernels
Compressible Euler equations interacting with incompressible flow
1. | Department of Mathematics, Imperial College London, London SW7 2AZ |
References:
[1] |
J. A. Carrillo, Y.-P. Choi and T. Karper, On the analysis of a coupled kinetic-fluid model with local alignment forces, to appear in Annales de lIHP-ANL.
doi: 10.1016/j.anihpc.2014.10.002. |
[2] |
J. A. Carrillo, Y.-P. Choi, E. Tadmor and C. Tan, Critical thresholds in 1D Euler equations with nonlocal forces, preprint, 2014. |
[3] |
J. A. Carrillo, R. Duan and A. Moussa, Global classical solutions close to the equilibrium to the Vlasov-Fokker-Planck-Euler system, Kinetic and Related Models, 4 (2011), 227-258.
doi: 10.3934/krm.2011.4.227. |
[4] |
J. A. Carrillo and T. Goudon, Stability and asymptotic analysis of a fluid-particle interaction model, Comm. Partial Differential Equations,, 31 (2006), 1349-1379.
doi: 10.1080/03605300500394389. |
[5] |
G.-Q. Chen, Euler equations and related hyperbolic conservation laws, in Handbook of Differential Equations, Vol. 2 (eds. C. M. Dafermos and E. Feireisl), Elsevier Science, Amsterdam, 2005, 1-104. |
[6] |
Y.-P. Choi, A revisit to the large-time behavior of the Vlasov/compressible Navier-Stokes equations, preprint, 2014. |
[7] |
R. Duan and S. Liu, Cauchy problem on the Vlaosv-Fokker-Planck equation coupled with the compressible Euler equations through the friction force, Kinetic and Related Models, 6 (2013), 687-700.
doi: 10.3934/krm.2013.6.687. |
[8] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. I, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-5364-8. |
[9] |
T. Goudon, P.-E. Jabin and A. Vasseur, Hydrodynamic limit for the Vlasov-Navier-Stokes equations. I. Light particles regime, Indiana Univ. Math. J., 53 (2004), 1495-1515.
doi: 10.1512/iumj.2004.53.2508. |
[10] |
T. Goudon, P.-E. Jabin and A. Vasseur, Hydrodynamic limit for the Vlasov-Navier-Stokes equations. II. Fine particles regime, Indiana Univ. Math. J., 53 (2004), 1517-1536.
doi: 10.1512/iumj.2004.53.2509. |
[11] |
T. Karper, A. Mellet and K. Trivisa, Hydrodynamic limit of the kinetic Cucker-Smale flocking model, Math. Mod. Meth. Appl. Sci., 25 (2015), 131-163.
doi: 10.1142/S0218202515500050. |
[12] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[13] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53, Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[14] |
A. Mellet and A. Vasseur, Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations, Math. Mod. Meth. Appl. Sci., 17 (2007), 1039-1063.
doi: 10.1142/S0218202507002194. |
[15] |
A. Mellet and A. Vasseur, Asymptotic analysis for a Vlasov-Fokker-Planck/Compressible Navier-Stokes equations, Comm. Math. Phys., 281 (2008), 573-596.
doi: 10.1007/s00220-008-0523-4. |
[16] |
T. C. Sideris, B. Thomases and D. Wang, Long time behavior of solutions to the 3D compressible Euler equations with damping, Comm. Partial Differential Equations, 28 (2003), 795-816.
doi: 10.1081/PDE-120020497. |
show all references
References:
[1] |
J. A. Carrillo, Y.-P. Choi and T. Karper, On the analysis of a coupled kinetic-fluid model with local alignment forces, to appear in Annales de lIHP-ANL.
doi: 10.1016/j.anihpc.2014.10.002. |
[2] |
J. A. Carrillo, Y.-P. Choi, E. Tadmor and C. Tan, Critical thresholds in 1D Euler equations with nonlocal forces, preprint, 2014. |
[3] |
J. A. Carrillo, R. Duan and A. Moussa, Global classical solutions close to the equilibrium to the Vlasov-Fokker-Planck-Euler system, Kinetic and Related Models, 4 (2011), 227-258.
doi: 10.3934/krm.2011.4.227. |
[4] |
J. A. Carrillo and T. Goudon, Stability and asymptotic analysis of a fluid-particle interaction model, Comm. Partial Differential Equations,, 31 (2006), 1349-1379.
doi: 10.1080/03605300500394389. |
[5] |
G.-Q. Chen, Euler equations and related hyperbolic conservation laws, in Handbook of Differential Equations, Vol. 2 (eds. C. M. Dafermos and E. Feireisl), Elsevier Science, Amsterdam, 2005, 1-104. |
[6] |
Y.-P. Choi, A revisit to the large-time behavior of the Vlasov/compressible Navier-Stokes equations, preprint, 2014. |
[7] |
R. Duan and S. Liu, Cauchy problem on the Vlaosv-Fokker-Planck equation coupled with the compressible Euler equations through the friction force, Kinetic and Related Models, 6 (2013), 687-700.
doi: 10.3934/krm.2013.6.687. |
[8] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. I, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-5364-8. |
[9] |
T. Goudon, P.-E. Jabin and A. Vasseur, Hydrodynamic limit for the Vlasov-Navier-Stokes equations. I. Light particles regime, Indiana Univ. Math. J., 53 (2004), 1495-1515.
doi: 10.1512/iumj.2004.53.2508. |
[10] |
T. Goudon, P.-E. Jabin and A. Vasseur, Hydrodynamic limit for the Vlasov-Navier-Stokes equations. II. Fine particles regime, Indiana Univ. Math. J., 53 (2004), 1517-1536.
doi: 10.1512/iumj.2004.53.2509. |
[11] |
T. Karper, A. Mellet and K. Trivisa, Hydrodynamic limit of the kinetic Cucker-Smale flocking model, Math. Mod. Meth. Appl. Sci., 25 (2015), 131-163.
doi: 10.1142/S0218202515500050. |
[12] |
T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[13] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53, Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[14] |
A. Mellet and A. Vasseur, Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations, Math. Mod. Meth. Appl. Sci., 17 (2007), 1039-1063.
doi: 10.1142/S0218202507002194. |
[15] |
A. Mellet and A. Vasseur, Asymptotic analysis for a Vlasov-Fokker-Planck/Compressible Navier-Stokes equations, Comm. Math. Phys., 281 (2008), 573-596.
doi: 10.1007/s00220-008-0523-4. |
[16] |
T. C. Sideris, B. Thomases and D. Wang, Long time behavior of solutions to the 3D compressible Euler equations with damping, Comm. Partial Differential Equations, 28 (2003), 795-816.
doi: 10.1081/PDE-120020497. |
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