參考文獻 |
[Eva98] L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics,
Volume 19, AMS, Providence, 1998.
[FNP01] E. Feireisl, A.Novotny and H. Petzeltova, On the Existence of Globally Defined
Weak Solutions to the Navier-Stokes Equations. J. Math. Fluid Mech. 3 (2001)
358–392.
[Fei04a] E. Feireisl, On the motion of a viscous, compressible, and heat conducting fluid.
Indiana Univ. Math. J., 53(6):1705-1738, 2004.
[Fei04b] E. Feireisl, Dynamics of viscous compressible fluids, Oxford University Press,
Oxford, 2004.
[FN09] E. Feireisl and A. Novotny, Singular Limits in Thermodynamics of Viscous Flu-
ids, Birkhauser Verlag, Basel, 2009.
[Gal94] G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes
equations, I. Springer-Verlag, New York, 1994.
[Hof87] D. Hoff, Global existence for 1D, compressible, isentropic Navier-Stokes equa-
tions with large initial data. Trans. Amer. Math. Soc., 303(1):169-181, 1987.
[Hof95] D. Hoff, Global solutions of the Navier-Stokes equations for multidimensional
compressible flow with discontinuous initial data. J. Differential Equations,
120(1):215-254, 1995.
[Hof98] D. Hoff, Global solutions of the equations of one-dimensional, compressible flow
with large data and forces, and with differing end states. Z. Angew. Math. Phys.,
49(5):774-785, 1998.
[HS01] D. Hoff and J. Smoller, Non-formation of vacuum states for com- pressible
Navier-Stokes equations. Comm. Math. Phys., 216(2):255–276, 2001.
[KS77] A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect
to time of initial-boundary value problems for one-dimensional equations of a
viscous gas. Prikl. Mat. Meh., 41(2):282-291, 1977.
[KJF77] A. Kufner, O. John, and S. Fucik, Function Spaces, Academia, Prague., 1977.
[Lio96] P. L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 1, Incompressible
models, Oxford University Press, Oxford, 1996.
[Lio98] P. L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible
models, Oxford University Press, Oxford, 1998.
[Lun95] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Prob-
lems. Birkhauser, Basel, 1995.
[MN79] A. Matsumura and T. Nishida, The initial value problem for the equations of
motion of compressible viscous and heat-conductive fluids. Proc. Japan Acad.
Ser. A Math. Sci., 55(9):337-342, 1979.
[Mur81] F. Murat, Compacite par compensation: condition necessaire et suffsante de
continuite faible sous une hypothese de rang constant, Ann. Sc. Norm Super.
Pisa, Cl. Sci., IV. Ser. 8 (1981), 69–102.
[NS04] A. Novotny and I. Straskraba, Introduction to the mathematical theory of com-
pressible flow. Oxford University Press, Oxford, 2004.
[Rud91] W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill Inc., New York, 1991.
[Ser86a] D. Serre, Solutions faibles globales des equations de Navier-Stokes pour un fluide
compressible. C. R. Acad. Sci. Paris Ser. I Math., 303(13):639-642, 1986.
[Ser86b] D. Serre, Sur l’equation monodimensionnelle d’un fluide visqueux, compressible
et conducteur de chaleur. C. R. Acad. Sci. Paris Ser. I Math., 303(14):703-706,
1986.
[She82] V. V. Shelukhin, Motion with a contact discontinuity in a viscous heat conduct-
ing gas. Dinamika Sploshn. Sredy, (57):131-152, 1982.
[She83] V. V. Shelukhin, Evolution of a contact discontinuity in the barotropic flow of
a viscous gas. Prikl. Mat. Mekh., 47(5):870-872, 1983.
[She84] V. V. Shelukhin, On the structure of generalized solutions of the one-dimensional
equations of a polytropic viscous gas. Prikl. Mat. Mekh., 48(6):912-920, 1984.
[She86] V. V. Shelukhin, Boundary value problems for equations of a barotropic viscous
gas with nonnegative initial density. Dinamika Sploshn. Sredy, (74):108-125,
162-163, 1986.
[Sim86] J. Simon, Compact sets in the space Lp
(0; T;B). Ann. Mat. Pura Appl. 146
(1986), 65-96.
[Sol76] V. A. Solonnikov, The solvability of the initial-boundary value problem for the
equations of motion of a viscous compressible fluid. Zap. Naucn. Sem. Leningrad.
Otdel. Mat. Inst. Steklov. (LOMI), 56:128-142, 197, 1976. Investigations on
linear operators and theory of functions, VI.
[Ste70] E.M. Stein, Singular integrals and differential properties of functions. Princeton
University Press, Princeton, 1970.
[Tem01] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, Ameri-
can Mathematical Society, 2001.
[Zie89] W.P. Ziemer, Weakly differentiable functions. Springer-Verlag, New York, 1989.
|