-
Previous Article
A system of the Hamilton--Jacobi and the continuity equations in the vanishing viscosity limit
- CPAA Home
- This Issue
-
Next Article
The Boltzmann equation near Maxwellian in the whole space
Free boundary problem for compressible flows with density--dependent viscosity coefficients
1. | Department of Mathematics, Zhejiang University, Hangzhou 310027, 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), 843-868.
doi: doi:10.1081/PDE-120020499. |
[2] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. Math. Phys., 238 (2003), 211-223. |
[3] |
G. Q. Chen and M. Kratka, Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary, Comm. Partial Differential Equations, 27 (2002), 907-943.
doi: doi:10.1081/PDE-120020499. |
[4] |
G. Q. Chen, Vacuum states and global stability of rarefaction waves for compressible flow, Methods Appl. Anal., 7 (2000), 337-361. |
[5] |
P. Chen and T. Zhang, A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients, Commun. Pure Appl. Anal., 7 (2008), 987-1016.
doi: doi:10.3934/cpaa.2008.7.987. |
[6] |
D. Y. Fang and T. Zhang, Compressible Navier-Stokes equations with vacuum state in one dimension, Commun. Pure Appl. Anal., 3 (2004), 675-694.
doi: doi:10.3934/cpaa.2004.3.675. |
[7] |
D. Y. Fang and T. Zhang, A note on compressible Navier-Stokes equations with vacuum state in one dimension, Nonlinear Anal., 58 (2004), 719-731.
doi: doi:10.1016/j.na.2004.05.016. |
[8] |
D. Y. Fang and T. Zhang, Global solutions of the Navier-Stokes equations for compressible flow with density-dependent viscosity and discontinuous initial data, J. Differential Equations, 222 (2006), 63-94.
doi: doi:10.1016/j.jde.2005.07.011. |
[9] |
Z. H. Guo, Q. S. Jiu and Z. P. Xin, Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, SIAM J. Math. Anal., 39 (2008), 1402-1427.
doi: doi:10.1137/070680333. |
[10] |
D. Hoff and D. Serre, The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow, SIAM J. Appl. Math., 51 (1991), 887-898.
doi: doi:10.1137/0151043. |
[11] |
D. Hoff, Discontinuous solutions of the Navier-Stokes equations for compressible flow, Arch. Rational Mech. Anal., 114 (1991), 15-46.
doi: doi:10.1007/BF00375683. |
[12] |
D. Hoff, Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data, J. Differential Equations, 95 (1992), 33-74.
doi: doi:10.1016/0022-0396(92)90042-L. |
[13] |
D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data, Indiana Univ. Math. J., 41 (1992), 1225-1302.
doi: doi:10.1512/iumj.1992.41.41060. |
[14] |
S. Jiang, Z. P. Xin and P. Zhang, Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity, Methods Appl. Anal., 12 (2005), 239-251. |
[15] |
S. Jiang and A. A. Zlotnik, Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data, Proc. Roy. Soc. Edinburgh Sect. A, 134 (2004), 939-960.
doi: doi:10.1017/S0308210500003565. |
[16] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics," Vol. 1-2. Oxford University Press: New York, 1996, 1998. |
[17] |
T. P. Liu, Z. P. Xin and T. Yang, Vacuum states for compressible flow, Discrete Contin. Dynam. Systems, 4 (1998), 1-32. |
[18] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equation, Comm. Partial Differential Equations, 32 (2007), 431-452.
doi: doi:10.1080/03605300600857079. |
[19] |
X. L. Qin, Z. A. Yao and H. X. Zhao, One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries, Comm. Pure Appl. Anal., 7 (2008), 373-381. |
[20] |
S. W. Vong, T. Yang and C. J. Zhu, Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum(II), J. Differential Equations, 192 (2003), 475-501.
doi: doi:10.1016/S0022-0396(03)00060-3. |
[21] |
V. A. Vaigant and A. V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscosity fluid, Siberian Math. J., 2 (1995), 1108-1141.
doi: doi:10.1007/BF02106835. |
[22] |
Z. P. Xin, Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density, Comm. Pure Appl. Math., 51 (1998), 229-240.
doi: doi:10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C. |
[23] |
T. Yang, Z. A. Yao and C. J. Zhu, Compressible Navier-Stokes equations with density-dependent viscosity and vacuum, Comm. Partial Differential Equations, 26 (2001), 965-981.
doi: doi:10.1081/PDE-100002385. |
[24] |
T. Yang and C. J. Zhu, Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum, Comm. Math. Phys., 230 (2002), 329-363.
doi: doi:10.1007/s00220-002-0703-6. |
[25] |
T. Zhang and D. Y. Fang, Global behavior of spherically symmetric Navier-Stokes equations with density-dependent viscosity, J. Differential Equations, 236 (2007), 293-341.
doi: doi:10.1016/j.jde.2007.01.025. |
[26] |
T. Zhang and D. Y. Fang, Global behavior of spherically symmetric Navier-Stokes-Poisson system with degenerate viscosity coefficients, Arch. Ration. Mech. Anal., 191 (2009), 195-243.
doi: doi:10.1007/s00205-008-0183-8. |
[27] |
T. Zhang and D. Y. Fang, A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, Nonlinear Analysis: Real World Applications, 10 (2009), 2272-2285.
doi: doi:10.1016/j.nonrwa.2008.04.014. |
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), 843-868.
doi: doi:10.1081/PDE-120020499. |
[2] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. Math. Phys., 238 (2003), 211-223. |
[3] |
G. Q. Chen and M. Kratka, Global solutions to the Navier-Stokes equations for compressible heat-conducting flow with symmetry and free boundary, Comm. Partial Differential Equations, 27 (2002), 907-943.
doi: doi:10.1081/PDE-120020499. |
[4] |
G. Q. Chen, Vacuum states and global stability of rarefaction waves for compressible flow, Methods Appl. Anal., 7 (2000), 337-361. |
[5] |
P. Chen and T. Zhang, A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients, Commun. Pure Appl. Anal., 7 (2008), 987-1016.
doi: doi:10.3934/cpaa.2008.7.987. |
[6] |
D. Y. Fang and T. Zhang, Compressible Navier-Stokes equations with vacuum state in one dimension, Commun. Pure Appl. Anal., 3 (2004), 675-694.
doi: doi:10.3934/cpaa.2004.3.675. |
[7] |
D. Y. Fang and T. Zhang, A note on compressible Navier-Stokes equations with vacuum state in one dimension, Nonlinear Anal., 58 (2004), 719-731.
doi: doi:10.1016/j.na.2004.05.016. |
[8] |
D. Y. Fang and T. Zhang, Global solutions of the Navier-Stokes equations for compressible flow with density-dependent viscosity and discontinuous initial data, J. Differential Equations, 222 (2006), 63-94.
doi: doi:10.1016/j.jde.2005.07.011. |
[9] |
Z. H. Guo, Q. S. Jiu and Z. P. Xin, Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, SIAM J. Math. Anal., 39 (2008), 1402-1427.
doi: doi:10.1137/070680333. |
[10] |
D. Hoff and D. Serre, The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible flow, SIAM J. Appl. Math., 51 (1991), 887-898.
doi: doi:10.1137/0151043. |
[11] |
D. Hoff, Discontinuous solutions of the Navier-Stokes equations for compressible flow, Arch. Rational Mech. Anal., 114 (1991), 15-46.
doi: doi:10.1007/BF00375683. |
[12] |
D. Hoff, Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data, J. Differential Equations, 95 (1992), 33-74.
doi: doi:10.1016/0022-0396(92)90042-L. |
[13] |
D. Hoff, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data, Indiana Univ. Math. J., 41 (1992), 1225-1302.
doi: doi:10.1512/iumj.1992.41.41060. |
[14] |
S. Jiang, Z. P. Xin and P. Zhang, Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity, Methods Appl. Anal., 12 (2005), 239-251. |
[15] |
S. Jiang and A. A. Zlotnik, Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data, Proc. Roy. Soc. Edinburgh Sect. A, 134 (2004), 939-960.
doi: doi:10.1017/S0308210500003565. |
[16] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics," Vol. 1-2. Oxford University Press: New York, 1996, 1998. |
[17] |
T. P. Liu, Z. P. Xin and T. Yang, Vacuum states for compressible flow, Discrete Contin. Dynam. Systems, 4 (1998), 1-32. |
[18] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equation, Comm. Partial Differential Equations, 32 (2007), 431-452.
doi: doi:10.1080/03605300600857079. |
[19] |
X. L. Qin, Z. A. Yao and H. X. Zhao, One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries, Comm. Pure Appl. Anal., 7 (2008), 373-381. |
[20] |
S. W. Vong, T. Yang and C. J. Zhu, Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum(II), J. Differential Equations, 192 (2003), 475-501.
doi: doi:10.1016/S0022-0396(03)00060-3. |
[21] |
V. A. Vaigant and A. V. Kazhikhov, On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscosity fluid, Siberian Math. J., 2 (1995), 1108-1141.
doi: doi:10.1007/BF02106835. |
[22] |
Z. P. Xin, Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density, Comm. Pure Appl. Math., 51 (1998), 229-240.
doi: doi:10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C. |
[23] |
T. Yang, Z. A. Yao and C. J. Zhu, Compressible Navier-Stokes equations with density-dependent viscosity and vacuum, Comm. Partial Differential Equations, 26 (2001), 965-981.
doi: doi:10.1081/PDE-100002385. |
[24] |
T. Yang and C. J. Zhu, Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum, Comm. Math. Phys., 230 (2002), 329-363.
doi: doi:10.1007/s00220-002-0703-6. |
[25] |
T. Zhang and D. Y. Fang, Global behavior of spherically symmetric Navier-Stokes equations with density-dependent viscosity, J. Differential Equations, 236 (2007), 293-341.
doi: doi:10.1016/j.jde.2007.01.025. |
[26] |
T. Zhang and D. Y. Fang, Global behavior of spherically symmetric Navier-Stokes-Poisson system with degenerate viscosity coefficients, Arch. Ration. Mech. Anal., 191 (2009), 195-243.
doi: doi:10.1007/s00205-008-0183-8. |
[27] |
T. Zhang and D. Y. Fang, A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, Nonlinear Analysis: Real World Applications, 10 (2009), 2272-2285.
doi: doi:10.1016/j.nonrwa.2008.04.014. |
[1] |
Xulong Qin, Zheng-An Yao, Hongxing Zhao. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Communications on Pure and Applied Analysis, 2008, 7 (2) : 373-381. doi: 10.3934/cpaa.2008.7.373 |
[2] |
Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041 |
[3] |
Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic and Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004 |
[4] |
Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133 |
[5] |
Quansen Jiu, Zhouping Xin. The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients. Kinetic and Related Models, 2008, 1 (2) : 313-330. doi: 10.3934/krm.2008.1.313 |
[6] |
Wuming Li, Xiaojun Liu, Quansen Jiu. The decay estimates of solutions for 1D compressible flows with density-dependent viscosity coefficients. Communications on Pure and Applied Analysis, 2013, 12 (2) : 647-661. doi: 10.3934/cpaa.2013.12.647 |
[7] |
Ping Chen, Ting Zhang. A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients. Communications on Pure and Applied Analysis, 2008, 7 (4) : 987-1016. doi: 10.3934/cpaa.2008.7.987 |
[8] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[9] |
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 |
[10] |
Wenjun Wang, Lei Yao. Spherically symmetric Navier-Stokes equations with degenerate viscosity coefficients and vacuum. Communications on Pure and Applied Analysis, 2010, 9 (2) : 459-481. doi: 10.3934/cpaa.2010.9.459 |
[11] |
Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602 |
[12] |
Mei Wang, Zilai Li, Zhenhua Guo. Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary. Communications on Pure and Applied Analysis, 2017, 16 (1) : 1-24. doi: 10.3934/cpaa.2017001 |
[13] |
Yuming Qin, Lan Huang, Shuxian Deng, Zhiyong Ma, Xiaoke Su, Xinguang Yang. Interior regularity of the compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 163-192. doi: 10.3934/dcdss.2009.2.163 |
[14] |
Tao Wang, Huijiang Zhao, Qingyang Zou. One-dimensional compressible Navier-Stokes equations with large density oscillation. Kinetic and Related Models, 2013, 6 (3) : 649-670. doi: 10.3934/krm.2013.6.649 |
[15] |
Zilai Li, Zhenhua Guo. On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3903-3919. doi: 10.3934/dcdsb.2017201 |
[16] |
Jishan Fan, Tohru Ozawa. An approximation model for the density-dependent magnetohydrodynamic equations. Conference Publications, 2013, 2013 (special) : 207-216. doi: 10.3934/proc.2013.2013.207 |
[17] |
Enrique Fernández-Cara. Motivation, analysis and control of the variable density Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2012, 5 (6) : 1021-1090. doi: 10.3934/dcdss.2012.5.1021 |
[18] |
Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure and Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675 |
[19] |
Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595 |
[20] |
Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609 |
2021 Impact Factor: 1.273
Tools
Metrics
Other articles
by authors
[Back to Top]