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Global weak solutions to the two-dimensional Navier-Stokes equations of compressible heat-conducting flows with symmetric data and forces
1. | College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 361000, China |
2. | Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-28, Beijing 100088 |
3. | Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China |
References:
[1] |
R. A. Adams and J. John, "Sobolev Space," $2^{nd}$ edition, Academic Press, New York, 2005. |
[2] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[3] |
R. Erban, On the existence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow, Math. Meth. Appl. Sci., 26 (2003), 489-517.
doi: 10.1002/mma.362. |
[4] |
E. Feireisl, "Dynamics of Viscous Compressible Fluids," Oxford Lecture Series in Mathematics and its Applications, 26, Oxford Univ. Press, Oxford, 2004. |
[5] |
E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not integrable, Comment. Math. Univ. Carolinae, 42 (2001), 83-98. |
[6] |
E. Feireisl and A. Novotnỳ, "Singular Limits in Thermodynamics of Viscous Fluids," Advances in Mathematical Fluid Mechanics, Birkhäuser Verlag, Basel, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[7] |
E. Feireisl, A. Novotnỳ and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[8] |
H. Frid and V. Shelukhin, Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry, SIAM J. Math. Anal., 31 (2000), 1144-1156.
doi: 10.1137/S003614109834394X. |
[9] |
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: 10.1512/iumj.1992.41.41060. |
[10] |
D. Hoff and H. K. Jenssen, Symmetric nonbarotropic flows with large data and forces, Arch. Rational Mech. Anal., 173 (2004), 297-343.
doi: 10.1007/s00205-004-0318-5. |
[11] |
F. Jiang and Z. Tan, On the domain dependence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow, Math. Meth. Appl. Sci., 32 (2009), 2350-2367.
doi: 10.1002/mma.1138. |
[12] |
S. Jiang and P. Zhang, Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids, J. Math. Pures Appl. (9), 82 (2003), 949-973.
doi: 10.1016/S0021-7824(03)00015-1. |
[13] |
S. Jiang and P. Zhang, On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, Comm. Math. Phys., 215 (2001), 559-581.
doi: 10.1007/PL00005543. |
[14] |
S. Jiang and P. Zhang, Remarks on weak solutions to the Navier-Stokes equations for 2-D compressible isothermal fluids with spherically symmetric initial data, Indiana Univ. Math. J., 51 (2002), 345-355.
doi: 10.1512/iumj.2002.51.2264. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[16] |
A. Kazhikhov and V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273-282. |
[17] |
A. Kufner, O. John and S. Fučik, "Function Spaces," Monographs and Textbooks on Mechanics of Solids and Fluids; Mechanics: Analysis, Noordhoff International Publ., Leyden; Academia, Prague, 1977. |
[18] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics. Vol. 2. Compressible Models," Oxford Lecture Series in Mathematics and its Applications, 10, Science Publications, The Clarendon Press, Oxford Univ. Press, New York, 1998. |
[19] |
J. Zhang, S. Jiang and F. Xie, Global weak solutions of an initial boundary value problem for screw pinches in plasma physics, Math. Models Meth. Appl. Sci., 19 (2009), 833-875.
doi: 10.1142/S0218202509003644. |
show all references
References:
[1] |
R. A. Adams and J. John, "Sobolev Space," $2^{nd}$ edition, Academic Press, New York, 2005. |
[2] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[3] |
R. Erban, On the existence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow, Math. Meth. Appl. Sci., 26 (2003), 489-517.
doi: 10.1002/mma.362. |
[4] |
E. Feireisl, "Dynamics of Viscous Compressible Fluids," Oxford Lecture Series in Mathematics and its Applications, 26, Oxford Univ. Press, Oxford, 2004. |
[5] |
E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not integrable, Comment. Math. Univ. Carolinae, 42 (2001), 83-98. |
[6] |
E. Feireisl and A. Novotnỳ, "Singular Limits in Thermodynamics of Viscous Fluids," Advances in Mathematical Fluid Mechanics, Birkhäuser Verlag, Basel, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[7] |
E. Feireisl, A. Novotnỳ and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[8] |
H. Frid and V. Shelukhin, Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry, SIAM J. Math. Anal., 31 (2000), 1144-1156.
doi: 10.1137/S003614109834394X. |
[9] |
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: 10.1512/iumj.1992.41.41060. |
[10] |
D. Hoff and H. K. Jenssen, Symmetric nonbarotropic flows with large data and forces, Arch. Rational Mech. Anal., 173 (2004), 297-343.
doi: 10.1007/s00205-004-0318-5. |
[11] |
F. Jiang and Z. Tan, On the domain dependence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow, Math. Meth. Appl. Sci., 32 (2009), 2350-2367.
doi: 10.1002/mma.1138. |
[12] |
S. Jiang and P. Zhang, Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids, J. Math. Pures Appl. (9), 82 (2003), 949-973.
doi: 10.1016/S0021-7824(03)00015-1. |
[13] |
S. Jiang and P. Zhang, On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations, Comm. Math. Phys., 215 (2001), 559-581.
doi: 10.1007/PL00005543. |
[14] |
S. Jiang and P. Zhang, Remarks on weak solutions to the Navier-Stokes equations for 2-D compressible isothermal fluids with spherically symmetric initial data, Indiana Univ. Math. J., 51 (2002), 345-355.
doi: 10.1512/iumj.2002.51.2264. |
[15] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[16] |
A. Kazhikhov and V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), 273-282. |
[17] |
A. Kufner, O. John and S. Fučik, "Function Spaces," Monographs and Textbooks on Mechanics of Solids and Fluids; Mechanics: Analysis, Noordhoff International Publ., Leyden; Academia, Prague, 1977. |
[18] |
P.-L. Lions, "Mathematical Topics in Fluid Mechanics. Vol. 2. Compressible Models," Oxford Lecture Series in Mathematics and its Applications, 10, Science Publications, The Clarendon Press, Oxford Univ. Press, New York, 1998. |
[19] |
J. Zhang, S. Jiang and F. Xie, Global weak solutions of an initial boundary value problem for screw pinches in plasma physics, Math. Models Meth. Appl. Sci., 19 (2009), 833-875.
doi: 10.1142/S0218202509003644. |
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