Global existence for a nuclear fluid in one dimension: the T > 0 case

Bernard Ducomet

Applications of Mathematics (2002)

  • Volume: 47, Issue: 1, page 45-75
  • ISSN: 0862-7940

Abstract

top
We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure P which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system, in the two cases P > 0 and P < 0 .

How to cite

top

Ducomet, Bernard. "Global existence for a nuclear fluid in one dimension: the $T>0$ case." Applications of Mathematics 47.1 (2002): 45-75. <http://eudml.org/doc/33102>.

@article{Ducomet2002,
abstract = {We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure $P$ which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system, in the two cases $P>0$ and $P<0$.},
author = {Ducomet, Bernard},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; compressible fluid; Navier-Stokes equations; compressible fluid},
language = {eng},
number = {1},
pages = {45-75},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global existence for a nuclear fluid in one dimension: the $T>0$ case},
url = {http://eudml.org/doc/33102},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Ducomet, Bernard
TI - Global existence for a nuclear fluid in one dimension: the $T>0$ case
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 1
SP - 45
EP - 75
AB - We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure $P$ which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system, in the two cases $P>0$ and $P<0$.
LA - eng
KW - Navier-Stokes equations; compressible fluid; Navier-Stokes equations; compressible fluid
UR - http://eudml.org/doc/33102
ER -

References

top
  1. 10.1038/305410a0, Nature 305 (1983), 410–412. (1983) DOI10.1038/305410a0
  2. 10.1103/PhysRevC.13.1226, Phys. Rev.  C 13 (1976), 1226–1258. (1976) DOI10.1103/PhysRevC.13.1226
  3. Nuclear Physics in one dimension, In: Nuclear Physics with Heavy Ions and Mesons, R. Balian et al. (eds.), North Holland, 1980. (1980) 
  4. Dynamics of nuclear fluids. I. Foundations, Nucl. Phys. A253 (1975), 469–489. (1975) 
  5. Simplified models of quantum fluids in nuclear physics, Math. Bohem. 126 (2001), 323–336. (2001) Zbl1050.76063MR1844272
  6. 10.1007/s000210050017, J. Math. Fluid Mech. 2 (2000), 1–15. (2000) Zbl0974.76013MR1755864DOI10.1007/s000210050017
  7. 10.1002/mma.227, Math. Methods Appl. Sci. 24 (2001), 543–559. (2001) MR1835486DOI10.1002/mma.227
  8. The Nuclear Many-Body Problem, Springer-Verlag, 1980. (1980) MR0611683
  9. Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. Studies in Mathematics and Its Applications Vol.  22, North Holland, Amsterdam, 1990. (1990) MR1035212
  10. 10.1016/0022-0396(85)90023-3, J. Differential Equations 58 (1985), 76–103. (1985) Zbl0579.35052MR0791841DOI10.1016/0022-0396(85)90023-3
  11. 10.1006/jdeq.1994.1064, J. Differential Equations 110 (1994), 157–181. (1994) Zbl0805.35074MR1278368DOI10.1006/jdeq.1994.1064
  12. 10.1007/BF02572324, Math. Z. 216 (1994), 317–336. (1994) MR1278427DOI10.1007/BF02572324
  13. 10.1051/m2an/1997310303811, RAIRO Modél. Math. Anal. Numér. 31 (1997), 381–407. (1997) Zbl0882.76025MR1451348DOI10.1051/m2an/1997310303811
  14. 10.1016/0362-546X(82)90058-X, Nonlinear Anal. Theory Methods Appl. 6 (1982), 435–454. (1982) MR0661710DOI10.1016/0362-546X(82)90058-X
  15. 10.1090/qam/1247437, Quart. Appl. Math. 51 (1993), 731–744. (1993) Zbl0809.35135MR1247437DOI10.1090/qam/1247437
  16. Large time behaviour of solutions to the equations of one-dimensional nonlinear thermoviscoelasticity, Quart. Appl. Math. 61 (1998), 201–219. (1998) MR1622554
  17. 10.1090/qam/1672183, Quart. Appl. Math. 57 (1999), 93–116. (1999) MR1672183DOI10.1090/qam/1672183
  18. On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math. 5 (1988), 53–85. (1988) Zbl0665.76076MR0924744
  19. 10.1016/0022-0396(82)90019-5, J. Differential Equations 44 (1982), 306–341. (1982) MR0657784DOI10.1016/0022-0396(82)90019-5

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.