-
Previous Article
On the Boltzmann equation with the symmetric stable Lévy process
- KRM Home
- This Issue
-
Next Article
Convergence rate for the method of moments with linear closure relations
Time periodic solutions of the non-isentropic compressible fluid models of Korteweg type
1. | School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China, China |
References:
[1] |
D. Bresch, B. Desjardins and C. K. Lin, On some compressible fluid models: Korteweg, lubrication and shallow water systems,, Comm. Partial Differential Equations, 28 (2003), 843.
doi: 10.1081/PDE-120020499. |
[2] |
Q. Chen and Z. Tan, Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamics equations,, Nonlinear Anal., 72 (2010), 4438.
doi: 10.1016/j.na.2010.02.019. |
[3] |
Z. Z. Chen, Q. H. Xiao and H. J. Zhao, Time periodic solutions of compressible fluid models of Korteweg type,, preprint, (). Google Scholar |
[4] |
R. Danchi, Global existence in critical space for compressible Navier-Stokes equations,, Invent.math., 141 (2000), 579.
doi: 10.1007/s002220000078. |
[5] |
R. Danchin and B. Desjardins, Existence of solutions for compressible fluid models of Korteweg type,, Ann. Inst. H. Poincare Anal. Nonlinear, 18 (2001), 97.
doi: 10.1016/S0294-1449(00)00056-1. |
[6] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal decay estimates on the linearized Boltzmann equations with time dependent force and their applications,, Comm. Math. Phys., 277 (2008), 189.
doi: 10.1007/s00220-007-0366-4. |
[7] |
B. Haspot, Existence of global weak solution for compressible fluid models of Korteweg type,, J. Math. Fluid Mech., 13 (2011), 223.
doi: 10.1007/s00021-009-0013-2. |
[8] |
B. Haspot, Existence of global strong solution for the compressible Navier-Stokes system and the Korteweg system in two-dimension,, Methods Appl. Anal., 20 (2013), 141.
doi: 10.4310/MAA.2013.v20.n2.a3. |
[9] |
H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type,, SIAM J. Math. Anal., 25 (1994), 85.
doi: 10.1137/S003614109223413X. |
[10] |
H. Hattori and D. Li, Golobal solutions of a high dimensional system for Korteweg materials,, J. Math. Anal. Appl., 198 (1996), 84.
doi: 10.1006/jmaa.1996.0069. |
[11] |
S. Kawashima, Systems of A Hyperbolic-parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics,, PhD thesis, (1983). Google Scholar |
[12] |
M. Kotschote, Strong solutions for a compressible fluid model of Korteweg type,, Ann. Inst. H. Poincare Anal. Nonlinear, 25 (2008), 679.
doi: 10.1016/j.anihpc.2007.03.005. |
[13] |
Y. P. Li, Global existence and optimal decay rate of the compressible Navier-Stokes-Korteweg equations with external force,, J. Math. Anal. Appl., 388 (2012), 1218.
doi: 10.1016/j.jmaa.2011.11.006. |
[14] |
H. F. Ma, S. Ukai and T. Yang, Time periodic solutions of compressible Navier-Stokes equations,, J. Differential Equations, 248 (2010), 2275.
doi: 10.1016/j.jde.2009.11.031. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fuids,, Proc. Japan Acad. Ser. A, 55 (1979), 337.
doi: 10.3792/pjaa.55.337. |
[16] |
A. Matsumura and T. Nishida, The initial value problems for the equations of motion of viscous and heat-conductive gases,, J. Math. Kyoto Univ., 20 (1980), 67.
|
[17] |
Z. Tan and H. Q. wang, Time periodic solutions of compressible magnetohydrodynamic equations,, Nonlinear Anal., 76 (2013), 153.
doi: 10.1016/j.na.2012.08.012. |
[18] |
Michael E. Taylor, Partial Differential Equations III,, Springer-Verlag, (1996).
doi: 10.1007/978-1-4757-4187-2. |
[19] |
S. Ukai, Time periodic solutions of Boltzmann equation,, Discrete Contin. Dyn. Syst., 14 (2006), 579.
doi: 10.3934/dcds.2006.14.579. |
[20] |
S. Ukai and T. Yang, The Boltzmann equation in the sapce $L^2\cap L^{\infty}_\beta$: global and time periodic solution,, Analysis and Applications, 4 (2006), 263.
doi: 10.1142/S0219530506000784. |
[21] |
Y. J. Wang and Z. Tan, Optimal decay rates for the compressible fluid models of Korteweg type,, J. Math. Anal. Appl., 379 (2011), 256.
doi: 10.1016/j.jmaa.2011.01.006. |
[22] |
G. J. Zhang, H. L. Li and C. J. Zhu, Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbbR^3$,, Journal of Differential Equations, 250 (2011), 866.
doi: 10.1016/j.jde.2010.07.035. |
[23] |
X. Zhang and Z. Tan, Decay estimates of the non-isentropic compressible fluid models of Korteweg type in $\mathbbR^3$,, Comm. Math. Sci., 12 (2014), 1437.
doi: 10.4310/CMS.2014.v12.n8.a4. |
show all references
References:
[1] |
D. Bresch, B. Desjardins and C. K. Lin, On some compressible fluid models: Korteweg, lubrication and shallow water systems,, Comm. Partial Differential Equations, 28 (2003), 843.
doi: 10.1081/PDE-120020499. |
[2] |
Q. Chen and Z. Tan, Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamics equations,, Nonlinear Anal., 72 (2010), 4438.
doi: 10.1016/j.na.2010.02.019. |
[3] |
Z. Z. Chen, Q. H. Xiao and H. J. Zhao, Time periodic solutions of compressible fluid models of Korteweg type,, preprint, (). Google Scholar |
[4] |
R. Danchi, Global existence in critical space for compressible Navier-Stokes equations,, Invent.math., 141 (2000), 579.
doi: 10.1007/s002220000078. |
[5] |
R. Danchin and B. Desjardins, Existence of solutions for compressible fluid models of Korteweg type,, Ann. Inst. H. Poincare Anal. Nonlinear, 18 (2001), 97.
doi: 10.1016/S0294-1449(00)00056-1. |
[6] |
R. J. Duan, S. Ukai, T. Yang and H. J. Zhao, Optimal decay estimates on the linearized Boltzmann equations with time dependent force and their applications,, Comm. Math. Phys., 277 (2008), 189.
doi: 10.1007/s00220-007-0366-4. |
[7] |
B. Haspot, Existence of global weak solution for compressible fluid models of Korteweg type,, J. Math. Fluid Mech., 13 (2011), 223.
doi: 10.1007/s00021-009-0013-2. |
[8] |
B. Haspot, Existence of global strong solution for the compressible Navier-Stokes system and the Korteweg system in two-dimension,, Methods Appl. Anal., 20 (2013), 141.
doi: 10.4310/MAA.2013.v20.n2.a3. |
[9] |
H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type,, SIAM J. Math. Anal., 25 (1994), 85.
doi: 10.1137/S003614109223413X. |
[10] |
H. Hattori and D. Li, Golobal solutions of a high dimensional system for Korteweg materials,, J. Math. Anal. Appl., 198 (1996), 84.
doi: 10.1006/jmaa.1996.0069. |
[11] |
S. Kawashima, Systems of A Hyperbolic-parabolic Composite Type, with Applications to the Equations of Magnetohydrodynamics,, PhD thesis, (1983). Google Scholar |
[12] |
M. Kotschote, Strong solutions for a compressible fluid model of Korteweg type,, Ann. Inst. H. Poincare Anal. Nonlinear, 25 (2008), 679.
doi: 10.1016/j.anihpc.2007.03.005. |
[13] |
Y. P. Li, Global existence and optimal decay rate of the compressible Navier-Stokes-Korteweg equations with external force,, J. Math. Anal. Appl., 388 (2012), 1218.
doi: 10.1016/j.jmaa.2011.11.006. |
[14] |
H. F. Ma, S. Ukai and T. Yang, Time periodic solutions of compressible Navier-Stokes equations,, J. Differential Equations, 248 (2010), 2275.
doi: 10.1016/j.jde.2009.11.031. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fuids,, Proc. Japan Acad. Ser. A, 55 (1979), 337.
doi: 10.3792/pjaa.55.337. |
[16] |
A. Matsumura and T. Nishida, The initial value problems for the equations of motion of viscous and heat-conductive gases,, J. Math. Kyoto Univ., 20 (1980), 67.
|
[17] |
Z. Tan and H. Q. wang, Time periodic solutions of compressible magnetohydrodynamic equations,, Nonlinear Anal., 76 (2013), 153.
doi: 10.1016/j.na.2012.08.012. |
[18] |
Michael E. Taylor, Partial Differential Equations III,, Springer-Verlag, (1996).
doi: 10.1007/978-1-4757-4187-2. |
[19] |
S. Ukai, Time periodic solutions of Boltzmann equation,, Discrete Contin. Dyn. Syst., 14 (2006), 579.
doi: 10.3934/dcds.2006.14.579. |
[20] |
S. Ukai and T. Yang, The Boltzmann equation in the sapce $L^2\cap L^{\infty}_\beta$: global and time periodic solution,, Analysis and Applications, 4 (2006), 263.
doi: 10.1142/S0219530506000784. |
[21] |
Y. J. Wang and Z. Tan, Optimal decay rates for the compressible fluid models of Korteweg type,, J. Math. Anal. Appl., 379 (2011), 256.
doi: 10.1016/j.jmaa.2011.01.006. |
[22] |
G. J. Zhang, H. L. Li and C. J. Zhu, Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbbR^3$,, Journal of Differential Equations, 250 (2011), 866.
doi: 10.1016/j.jde.2010.07.035. |
[23] |
X. Zhang and Z. Tan, Decay estimates of the non-isentropic compressible fluid models of Korteweg type in $\mathbbR^3$,, Comm. Math. Sci., 12 (2014), 1437.
doi: 10.4310/CMS.2014.v12.n8.a4. |
[1] |
Zhong Tan, Yong Wang, Xu Zhang. Large time behavior of solutions to the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbb{R}^{3}$. Kinetic & Related Models, 2012, 5 (3) : 615-638. doi: 10.3934/krm.2012.5.615 |
[2] |
Wenjun Wang, Weike Wang. Decay rates of the compressible Navier-Stokes-Korteweg equations with potential forces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 513-536. doi: 10.3934/dcds.2015.35.513 |
[3] |
Hong Cai, Zhong Tan, Qiuju Xu. Time periodic solutions to Navier-Stokes-Korteweg system with friction. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 611-629. doi: 10.3934/dcds.2016.36.611 |
[4] |
Zhong Tan, Leilei Tong. Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$. Kinetic & Related Models, 2018, 11 (1) : 191-213. doi: 10.3934/krm.2018010 |
[5] |
Tong Tang, Hongjun Gao. On the compressible Navier-Stokes-Korteweg equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2745-2766. doi: 10.3934/dcdsb.2016071 |
[6] |
Yingshan Chen, Shijin Ding, Wenjun Wang. Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5287-5307. doi: 10.3934/dcds.2016032 |
[7] |
Haibo Cui, Zhensheng Gao, Haiyan Yin, Peixing Zhang. Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4839-4870. doi: 10.3934/dcds.2016009 |
[8] |
Weike Wang, Xin Xu. Large time behavior of solution for the full compressible navier-stokes-maxwell system. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2283-2313. doi: 10.3934/cpaa.2015.14.2283 |
[9] |
Xiangdi Huang, Zhouping Xin. On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4477-4493. doi: 10.3934/dcds.2016.36.4477 |
[10] |
Jianwei Yang, Peng Cheng, Yudong Wang. Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity. Electronic Research Announcements, 2015, 22: 20-31. doi: 10.3934/era.2015.22.20 |
[11] |
Zhong Tan, Xu Zhang, Huaqiao Wang. Asymptotic behavior of Navier-Stokes-Korteweg with friction in $\mathbb{R}^{3}$. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2243-2259. doi: 10.3934/dcds.2014.34.2243 |
[12] |
Jing Wang, Feng Xie. On the Rayleigh-Taylor instability for the compressible non-isentropic inviscid fluids with a free interface. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2767-2784. doi: 10.3934/dcdsb.2016072 |
[13] |
J. Huang, Marius Paicu. Decay estimates of global solution to 2D incompressible Navier-Stokes equations with variable viscosity. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4647-4669. doi: 10.3934/dcds.2014.34.4647 |
[14] |
Moez Daoulatli. Rates of decay for the wave systems with time dependent damping. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 407-443. doi: 10.3934/dcds.2011.31.407 |
[15] |
Matthew Paddick. The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2673-2709. doi: 10.3934/dcds.2016.36.2673 |
[16] |
Grzegorz Karch, Xiaoxin Zheng. Time-dependent singularities in the Navier-Stokes system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3039-3057. doi: 10.3934/dcds.2015.35.3039 |
[17] |
Ryo Ikehata, Shingo Kitazaki. Optimal energy decay rates for some wave equations with double damping terms. Evolution Equations & Control Theory, 2019, 8 (4) : 825-846. doi: 10.3934/eect.2019040 |
[18] |
Qing Chen, Zhong Tan. Time decay of solutions to the compressible Euler equations with damping. Kinetic & Related Models, 2014, 7 (4) : 605-619. doi: 10.3934/krm.2014.7.605 |
[19] |
Jiang Xu, Wen-An Yong. Zero-relaxation limit of non-isentropic hydrodynamic models for semiconductors. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1319-1332. doi: 10.3934/dcds.2009.25.1319 |
[20] |
Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207 |
2018 Impact Factor: 1.38
Tools
Metrics
Other articles
by authors
[Back to Top]