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Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations
1. | Department of Mathematics, South China University of Technology, Guangzhou 510641 |
2. | Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631 |
3. | College of Science, University of Shanghai for Science and Technology, Shanghai 200093 |
References:
[1] | |
[2] |
J. Ballew, Low Mach number limits to the Navier-Stokes-Smoluchowski system, Hyperbolic Problems: Theory, Numerics, Applications. AIMS Series on Applied Mathematics, 8 (2014), 301-308. |
[3] |
C. Baranger, L. Boudin, P. E. Jabin and S. Mancini, A modeling of biospray for the upper airways, CEMRACS 2004-mathematics and applications to biology and medicine, ESAIM Proc, 14 (2005), 41-47. |
[4] |
J. Ballew and K. Trivisa, Weakly dissipative solutions and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system, Nonlinear Analysis Series A: Theory, Methods Applications, 91 (2013), 1-19.
doi: 10.1016/j.na.2013.06.002. |
[5] |
S.Berres, R.Bürger, K. H. Karlsen and E. M. Tory, Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression, SIAM J. Appl. Math., 64 (2003), 41-80.
doi: 10.1137/S0036139902408163. |
[6] |
J. A. Carrillo and T. Goudon, Stability and asymptotic analysis of a fluid-particle interaction model, Commun. Partial Differ. Equ., 31 (2006), 1349-1379.
doi: 10.1080/03605300500394389. |
[7] |
J. A. Carrillo, T. Karper and K. Trivisa, On the dynamics of a fluid-particle interaction model: the bubbling regime, Nonlinear Anal, 74 (2011), 2778-2801.
doi: 10.1016/j.na.2010.12.031. |
[8] |
T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, American Mathematical Society, 2003. |
[9] |
S. J. Ding, B. Y. Huang and H. Y. Wen, Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum, preprint, 2015, http://202.116.32.252:8080/maths/uploadfile/2015/1212/20151212030124241.pdf. |
[10] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal convergence rates for the compressible Navier-Stokes equations with potential forces, Math. Models Methods Appl. Sci., 17 (2007), 737-758.
doi: 10.1142/S021820250700208X. |
[11] |
D. Y. Fang, R. Z. Zi and T. Zhang, Global classical large solutions to a 1D fluid-particle interaction model: The bubbling regime, J. Math. Phys, 53 (2012), 033706, 21pp.
doi: 10.1063/1.3693979. |
[12] |
D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (1995), 603-676.
doi: 10.1512/iumj.1995.44.2003. |
[13] |
N. Ju, Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space, Comm. Math. Phys., 251 (2004), 365-376.
doi: 10.1007/s00220-004-1062-2. |
[14] |
S. Kawashima, Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations in Magnetohydrodynamics, Kyoto University, 1983. |
[15] |
T. Kobayashi and Y. Shibata, Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in $\mathbbR^3$, Comm. Math. Phys., 200 (1999), 621-659.
doi: 10.1007/s002200050543. |
[16] |
P. L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 2, Compressible Models, Oxford University Press, Oxford, 1998. |
[17] |
A. Matsumura and T. Nishida, Initial boundary problems for the equations of motion of compressible viscous and heat-conducive fluids, Commun. Math. Phys., 89 (1983), 445-464.
doi: 10.1007/BF01214738. |
[18] |
Y. K. Song, H. J. Yuan, Y. Chen and Z. D. Guo, Strong solutions for a 1D fluid-particle interaction non-newtonian model: The bubbling regime, J. Math. Phys., 54 (2013), 091501, 12pp.
doi: 10.1063/1.4820446. |
[19] |
I. Vinkovic, C. Aguirre, S. Simoëns and M. Gorokhovski, Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow, International Journal of Multiphase Flow, 32 (2006), 344-364.
doi: 10.1016/j.ijmultiphaseflow.2005.10.005. |
[20] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Differential Equations, 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[21] |
F. A. Williams, Combustion Theory, Benjamin Cummings Publ., 1985. |
[22] |
F. A. Williams, Spray combustion and atomization, Phys. Fluids, 1 (1958), 541-555.
doi: 10.1063/1.1724379. |
[23] |
J. W. Zhang and J. N. Zhao, Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics, Commun. Math. Sci., 8 (2010), 835-850.
doi: 10.4310/CMS.2010.v8.n4.a2. |
show all references
References:
[1] | |
[2] |
J. Ballew, Low Mach number limits to the Navier-Stokes-Smoluchowski system, Hyperbolic Problems: Theory, Numerics, Applications. AIMS Series on Applied Mathematics, 8 (2014), 301-308. |
[3] |
C. Baranger, L. Boudin, P. E. Jabin and S. Mancini, A modeling of biospray for the upper airways, CEMRACS 2004-mathematics and applications to biology and medicine, ESAIM Proc, 14 (2005), 41-47. |
[4] |
J. Ballew and K. Trivisa, Weakly dissipative solutions and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system, Nonlinear Analysis Series A: Theory, Methods Applications, 91 (2013), 1-19.
doi: 10.1016/j.na.2013.06.002. |
[5] |
S.Berres, R.Bürger, K. H. Karlsen and E. M. Tory, Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression, SIAM J. Appl. Math., 64 (2003), 41-80.
doi: 10.1137/S0036139902408163. |
[6] |
J. A. Carrillo and T. Goudon, Stability and asymptotic analysis of a fluid-particle interaction model, Commun. Partial Differ. Equ., 31 (2006), 1349-1379.
doi: 10.1080/03605300500394389. |
[7] |
J. A. Carrillo, T. Karper and K. Trivisa, On the dynamics of a fluid-particle interaction model: the bubbling regime, Nonlinear Anal, 74 (2011), 2778-2801.
doi: 10.1016/j.na.2010.12.031. |
[8] |
T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, American Mathematical Society, 2003. |
[9] |
S. J. Ding, B. Y. Huang and H. Y. Wen, Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum, preprint, 2015, http://202.116.32.252:8080/maths/uploadfile/2015/1212/20151212030124241.pdf. |
[10] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal convergence rates for the compressible Navier-Stokes equations with potential forces, Math. Models Methods Appl. Sci., 17 (2007), 737-758.
doi: 10.1142/S021820250700208X. |
[11] |
D. Y. Fang, R. Z. Zi and T. Zhang, Global classical large solutions to a 1D fluid-particle interaction model: The bubbling regime, J. Math. Phys, 53 (2012), 033706, 21pp.
doi: 10.1063/1.3693979. |
[12] |
D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (1995), 603-676.
doi: 10.1512/iumj.1995.44.2003. |
[13] |
N. Ju, Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space, Comm. Math. Phys., 251 (2004), 365-376.
doi: 10.1007/s00220-004-1062-2. |
[14] |
S. Kawashima, Systems of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations in Magnetohydrodynamics, Kyoto University, 1983. |
[15] |
T. Kobayashi and Y. Shibata, Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in $\mathbbR^3$, Comm. Math. Phys., 200 (1999), 621-659.
doi: 10.1007/s002200050543. |
[16] |
P. L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 2, Compressible Models, Oxford University Press, Oxford, 1998. |
[17] |
A. Matsumura and T. Nishida, Initial boundary problems for the equations of motion of compressible viscous and heat-conducive fluids, Commun. Math. Phys., 89 (1983), 445-464.
doi: 10.1007/BF01214738. |
[18] |
Y. K. Song, H. J. Yuan, Y. Chen and Z. D. Guo, Strong solutions for a 1D fluid-particle interaction non-newtonian model: The bubbling regime, J. Math. Phys., 54 (2013), 091501, 12pp.
doi: 10.1063/1.4820446. |
[19] |
I. Vinkovic, C. Aguirre, S. Simoëns and M. Gorokhovski, Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow, International Journal of Multiphase Flow, 32 (2006), 344-364.
doi: 10.1016/j.ijmultiphaseflow.2005.10.005. |
[20] |
Y. J. Wang, Decay of the Navier-Stokes-Poisson equations, J. Differential Equations, 253 (2012), 273-297.
doi: 10.1016/j.jde.2012.03.006. |
[21] |
F. A. Williams, Combustion Theory, Benjamin Cummings Publ., 1985. |
[22] |
F. A. Williams, Spray combustion and atomization, Phys. Fluids, 1 (1958), 541-555.
doi: 10.1063/1.1724379. |
[23] |
J. W. Zhang and J. N. Zhao, Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics, Commun. Math. Sci., 8 (2010), 835-850.
doi: 10.4310/CMS.2010.v8.n4.a2. |
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