Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 289-311.doi: 10.1016/S0252-9602(10)60046-X
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QIN Yu-Ming, SONG Jin-Ping
Received:
2006-11-12
Revised:
2008-01-31
Online:
2010-01-20
Published:
2010-01-20
Supported by:
This work was supported in part by the NSF of China (10571024, 10871040) and the grant of Prominent Youth
of Henan Province of China (0412000100).
CLC Number:
QIN Yu-Ming, SONG Jin-Ping. MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID[J].Acta mathematica scientia,Series B, 2010, 30(1): 289-311.
[1] Antontsev S N, Kazhikhov A V, Monakhov V N. Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. Studies in Mathematics and its Applications, Vol 22. Amsterdam, New York: North-Holland Publishing Co, 1990 [2] Chen G. Global solutions to the compressible Navier-Stokes equations for a reacting mixture. SIAM J Math Anal, 1992, 3: 609--634 [3] Deckelnick K. L2 Decay for the compressible Navier-Stokes equations in unbounded domains. Comm Partial Differ Equ, 1993, 18: 1445--1476 [4] Feireisl E. The dynamical systems approach to the Navier-Stokes equations of compressible fluid. Preprint [5] Feireisl E. Global attractors for the Navier-Stokes equations of three-dimensional compressible flow. C R Acad Sci Paris Sèr I, 2000, 331: 35--39 [6] Foias C, Temam R. The Connection Between the Navier-Stokes Equations, Dynamical Systems and Turbulence//Crandall M G, Rabinowitz P H, Turner R E L, eds. Directions in Partial Differential Equations. [7] Fujita-Yashima H, Benabidallah R. Unicite' de la solution de l'\'equation monodimensionnelle ou a' symètrie sphèrique d'un gaz visqueux et calorifère. Rendi del Circolo Mat di Palermo Ser II, 1993, 42: 195--218 [8] Fujita-Yashima H, Benabidallah R. Equationá symètrie sphèrique d'un gaz visqueux et calorifère avec la surface libre. Annali Mat pura ed applicata, 1995, 168: 75--117 [9] Ghidaglia J M. Finite dimensional behaviour for weakly damped driven Schrödinger equations. Ann Inst Henri Poincarè, 1988, 5: 365--405 [10] Hale J K. Asymptotic Behaviour of Dissipative Systems. Mathematical Surveys and Monographs, Number 25. Providence, Rhode Island: American Mathematical Society, 1988 [11] Hale J K, Perissinotto Jr A. Global attractor and convergence for one-dimensional semilinear thermoelasticity. Dynamic Systems and Applications, 1993, 2: 1--9 [12] Hoff D. Global well-posedness of the Cauchy problem for the Navire-Stokes equations of nonisentropic flow with discontinuous initial data. J Diff Eqs, 1992, 95: 33--74 [13] Hoff D, Ziane M. Compact attractors for the Navier--Stokes equations of one-dimensional compressible flow. C R Acad Sci Paris Ser I, 1999, 328: 239--244 [14] Hoff D, Ziane M. The global attractor and finite determining nodes for the Navier--Stokes equations of compressible flow with singular initial data. Indiana Univ Math J, 2000, 49: 843--889 [15] Hsiao L, Luo T. Large-time behaviour of solutions for the outer pressure problem of a viscous heat-onductive one-dimensional real gas. Proc Roy Soc Edinburgh Sect A, 1996, 126: 1277--1296 [16] Jiang S. On the asymptotic behaviour of the motion of a viscous, heat-conducting, one-dimensional real gas. Math Z, 1994, 216: 317--336 [17] Jiang S. Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain. Comm Math Phys, 1996, 178: 339--374 [18] Jiang S. Large-time behavior of solutions to the equations of a viscous polytropic ideal gas. Ann Mate Pura Appl, 1998, 175: 253--275 [19] Kawashima S, Nishida T. Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases. J Math Kyoto Univ, 1981, 21: 825--837 [20] Kazhikhov A V. To a theory of boundary value problems for equations of one-dimensional nonstationary motion of viscous heat-conduction gases. Din Sploshn Sredy, 1981, 50: 37--62 (in Russion) [21] Kazhikhov A V. Cauchy problem for viscous gas equations. Siberian Math J, 1982, 23: 44--49 [22] Kazhikhov A V, Shelukhin V V. Unique global solution with respect to time of initial boundary value problems for one-dimensional equations of a viscous gas. J Appl Math Mech, 1977, 41: 273--282 [23] Lions P L. Mathematical Topics in Fluid Dynamics: Vol 2: Compressible Models. Oxford Lecutre Series in Mathematics and its Applications, Vol 2, No 10. Oxford: Oxford Science Publication, 1998 [24] Matsumura A, Nishida T. The initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Proc Japan Acad Ser A, 1979, 55: 337--342 [25] Matsumura A, Nishida T. The initial boundary value problems for the equations of motion of compressible viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20: 67--104 [26] Matsumura A, Nishida T. Initial boundary value problems for the equations of motion of general fluids//Glowinski G, Lions J L, eds. Computing Meth in Appl Sci and Engin V. Amsterdam: NorthHolland, 1982: 389--406 [27] Matsumura A, Nishida T. Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Comm Math Phys, 1983, 89: 445--464 [28] Matsumura A, Nishida T. The initial value problem for the equations of motion of compressible viscous and heat-conductive gases. Proc Japan Acad Ser A, 1979, 55: 337--342 [29] Matsumura A, Nishida T. The initial value problem for the equations of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20: 67--104 [30] Nagasawa T. On the one-dimensinal motion of the polytropic ideal gas non-fixed on the boundary. J Diff Equ, 1986, 65: 49--67 [31] Nikolaev V B. On the solvability of mixed problem for one-dimensional axisymmetrical viscous gas flow. Dinamicheskie zadachi Mekhaniki sploshnoj sredy, 63 Sibirsk. Otd Acad Nauk SSSR, Inst Gidrodinamiki, 1983 (Russian) [32] Okada M, Kawashima S. On the equations of one-dimensional motion of compressible viscous fluids. J Math Kyoto Univ, 1983, 23: 55--71 [33] Padula M. Stability properties of regular flows of heat-conducting compressible fluids. J Math Kyoto Univ, 1992, 32: 401--442 [34] Qin Y. Global existence and asymptotic behaviour of solutions to a system of equations for a nonlinear one-dimensional viscous heat-conducting real gas. Chin Ann Math, 1999, 20A(3): 343--354 (in Chinese) [35] Qin Y. Global existence and asymptotic behaviour of solutions to nonlinear hyperbolic-parabolic coupled systems with arbitrary initial data[D]. Fudan University, 1998 [36] Qin Y. Global existence and asymptotic behaviour for the solutions to nonlinear viscous, heat-conductive, one-dimensional real gas. Adv Math Sci Appl, 2000, 10: 119--148 [37] Qin Y. Global existence and asymptotic behaviour for a viscous, heat-conductive, one-dimensional real gas with fixed and thermally insulated endpoints. Nonlinear Analysis TMA, 2001, 44: 413--441 [38] Qin Y. Global existence and asymptotic behaviour of solution to the system in one-dimensional nonlinear thermoviscoelasticity. Quart Appl Math, 2001, 59: 113--142 [39] Qin Y. Global existence and asymptotic behaviour for a viscous, heat-conductive, one-dimensional real gas with fixed and constant temperature boundary conditions. Adv Diff Eqs, 2002, 7: 129--154 [40] Qin Y. Exponential stability for the compressible Navier--Stokes equations. preprint [41] Qin Y. Exponential stability for a nonlinear one-dimensional heat-conductive viscous real gas. J Math Anal Appl, 2002, 272: 507--535 [42] Qin Y, Ma T, Cavalcanti M M, Andrade D. Exponential stability in H4 for the Navier--Stokes equations of compressible and heat-conductive fluid. Comm Pure Appl Anal, 2005, 4: 635--664 [43] Qin Y, Rivera J M. Universal attractors for a nonlinear one-dimensional heat-conductive viscous real gas. [44] Radke R, Zheng S. Global existence and asymptotic behaviour in nonlinear thermoviscoelasticity. J Diff Eqs, 1997, 134: 46--67 [45] Sell G R. Global attractors for the three-dimensional Navier-Stokes equations. J Dynam Diff Eqs, 1996, 8: 1--33 [46] When W, Zheng S. Maximal attractor for the coupled Cahn-Hilliard Equations. Nonlinear Analysis TMA, 2002, 49: 21--34 [47] Shen W, Zheng S, Zhu P. Global existence and asymptotic behaviour of weak solutions to nonlinear thermoviscoelastic system with clamped boundary conditions. Quart Appl Math, 1999, 57: 93--116 [48] Sprekels J, Zheng S. Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys. Physica D, 1998, 121: 252--262 [49] Sprekels J, Zheng S, Zhu P. Asymptotic behaviour of the solutions to a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys. SIAM J Math Anal, 1998, 29: 69--84 [50] Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Appl Math Sci, Vol 68. New York: Springer-Verlag, 1988 [51] Valli A, Zajaczkowski W M. Navier-Stokes Equations for compressible fluids: global existence and qualitative properties of the solutions in the general case. Comm Math Phys, 1986, 103: 259--296 [52] Zheng S. Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems. Pitman Series Monographs and Surveys in Pure and Applied Mathematics, Vol 76. London: Longman Group Limited, 1995 [53] Zheng S, Qin Y. Maximal attractor for the system of one-dimensional polytropic viscous ideal gas. Quart Appl Math, 2001, 59: 579--599 [54] Zheng S, Qin Y. Universal attractors for the Navier-Stokes equations of compressible and heat-conductive fluid in bounded annular domains in Rn. Arch Rational Mech Anal, 2001, 160: 153--179 [55] Zheng S, Shen W. Global solutions to the Cauchy problem of the equations of one-dimensional thermoviscoelasticity. J Partial Differ Equ, 1989, 2: 26--38 |
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