Global existence for a nuclear fluid in one dimension: the \(T>0\) case. (English) Zbl 1090.76517

A simplified one-dimensional thermal model of nuclear matter described by a system of Navier-Stokes type is considered. A global existence result for large data with a free boundary is established. Nonmonotonicity of the state equation due to an effective nuclear interaction is admitted.


76D05 Navier-Stokes equations for incompressible viscous fluids
76N15 Gas dynamics (general theory)
Full Text: DOI EuDML


[1] P. J. Siemens: Liquid-gas phase transition in nuclear matter. Nature 305 (1983), 410-412.
[2] P. Bonche, S. Koonin and J. W. Negele: One-dimensional nuclear dynamics in the TDHF approximation. Phys. Rev. C 13 (1976), 1226-1258.
[3] D. K. Campbell: Nuclear Physics in one dimension. Nuclear Physics with Heavy Ions and Mesons, R. Balian et al. (eds.), North Holland, 1980.
[4] C. Y. Wong, J. A. Maruhn and T. A. Welton: Dynamics of nuclear fluids. I. Foundations. Nucl. Phys. A253 (1975), 469-489.
[5] B. Ducomet: Simplified models of quantum fluids in nuclear physics. Math. Bohem. 126 (2001), 323-336. · Zbl 1050.76063
[6] B. Ducomet: Global existence for a simplified model of nuclear fluid in one dimension. J. Math. Fluid Mech. 2 (2000), 1-15. · Zbl 0974.76013
[7] B. Ducomet: Asymptotic behaviour for a nuclear fluid in one dimension. Math. Methods Appl. Sci. 24 (2001), 543-559. · Zbl 0973.35150
[8] P. Ring, P. Schuck: The Nuclear Many-Body Problem. Springer-Verlag, 1980.
[9] S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov: Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. Studies in Mathematics and Its Applications Vol. 22. North Holland, Amsterdam, 1990. · Zbl 0696.76001
[10] B. Kawohl: Global existence of large solutions to initial boundary value problems for a viscous heat-conducting one-dimensional real gas. J. Differential Equations 58 (1985), 76-103. · Zbl 0579.35052
[11] S. Jiang: On initial boundary value problems for a viscous heat-conducting one-dimensional real gas. J. Differential Equations 110 (1994), 157-181. · Zbl 0805.35074
[12] S. Jiang: On the asymptotic behaviour of the motion of a viscous heat-conducting, one-dimensional real gas. Math. Z. 216 (1994), 317-336. · Zbl 0807.35016
[13] B. Ducomet: On the stability of a stellar structure in one dimension II: The reactive case. RAIRO Modél. Math. Anal. Numér. 31 (1997), 381-407. · Zbl 0882.76025
[14] C. Dafermos, L. Hsiao: Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity. Nonlinear Anal. Theory Methods Appl. 6 (1982), 435-454. · Zbl 0498.35015
[15] S. Jiang: Global large solutions to initial boundary value problems in one-dimensional nonlinear thermoviscoelasticity. Quart. Appl. Math. 51 (1993), 731-744. · Zbl 0809.35135
[16] L. Hsiao, T. Luo: Large time behaviour of solutions to the equations of one-dimensional nonlinear thermoviscoelasticity. Quart. Appl. Math. 61 (1998), 201-219. · Zbl 0981.74011
[17] W. Shen, S. Zheng and P. Zhu: Global existence and asymptotic behaviour of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions. Quart. Appl. Math. 57 (1999), 93-116. · Zbl 1025.74014
[18] T. Nagasawa: On the outer pressure problem of the one-dimensional polytropic ideal gas. Japan J. Appl. Math. 5 (1988), 53-85. · Zbl 0665.76076
[19] G. Andrews, J. M. Ball: Asymptotic behaviour and changes of phase in one-dimensional non linear viscoelasticity. J. Differential Equations 44 (1982), 306-341. · Zbl 0501.35011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.