×

Global solvability of the free-boundary problem for one-dimensional motion of a self-gravitating viscous radiative and reactive gas. (English) Zbl 1152.35520

Summary: We consider a free-boundary system describing the one-dimensional motion of a self-gravitating, radiative and chemically reactive gas. For arbitrary large smooth initial data, we prove the unique existence, global in time, of a classical solution of the corresponding problem with fixed domain, obtained by the Lagrangian mass transformation.

MSC:

35R30 Inverse problems for PDEs
35Q30 Navier-Stokes equations
76N15 Gas dynamics (general theory)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] B. Ducomet, Some stability results for reactive Navier-Stokes-Poisson systems, in Evolution equations: existence, regularity and singularities (Warsaw, 1998) , 83-118, Polish Acad. Sci., Polish Scientific Publishers, Warsaw, 2000. · Zbl 0958.35110
[2] B. Ducomet and A. Zlotnik, Lyapunov functional method for 1D radiative and reactive viscous gas dynamics, Arch. Ration. Mech. Anal. 177 (2005), no. 2, 185-229. · Zbl 1070.76044 · doi:10.1007/s00205-005-0363-8
[3] B. Ducomet and A. Zlotnik, On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics, Nonlinear Anal. 63 (2005), no. 8, 1011-1033. · Zbl 1083.35109 · doi:10.1016/j.na.2005.03.064
[4] A. V. Kazhikhov, To the theory of boundary value problems for equations of a one-dimensional non-stationary motion of a viscous heat-conductive gas, Din. Sploshn. Sredy 50 (1981), 37-62. (in Russian). · Zbl 0515.76076
[5] A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of the initial-boundary value problems for one-dimensional equations of a viscous gas, J. Appl. Math. Mech. 41 (1977), no. 2, 273-282.; translated from Prikl. Mat. Meh. 41 (1977), no. 2, 282-291. · Zbl 0393.76043 · doi:10.1016/0021-8928(77)90011-9
[6] O. A. Lady\uzhenskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and quasi-linear equations of parabolic type , Transl. Math. Monogr., vol. 23, Amer. Math. Soc., Providence, RI, 1968. · Zbl 0174.15403
[7] T. Nagasawa, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math. 5 (1988), no. 1, 53-85. · Zbl 0665.76076 · doi:10.1007/BF03167901
[8] P. Secchi, On the motion of gaseous stars in the presence of radiation, Comm. Partial Differential Equations 15 (1990), no. 2, 185-204. · Zbl 0708.35096 · doi:10.1080/03605309908820683
[9] S. F. Shandarin and Ya. B. Zel’dovich, The large-scale structure of the universe: turbulence, intermittency, structures in a self-gravitating medium, Rev. Modern Phys. 61 (1989), no. 2, 185-220. · doi:10.1103/RevModPhys.61.185
[10] A. Tani, On the first initial-boundary value problem of compressible viscous fluid motion, Publ. Res. Inst. Math. Sci. 13 (1977), 193-253. · Zbl 0366.35070 · doi:10.2977/prims/1195190106
[11] A. Tani, On the free boundary value problem for compressible viscous fluid motion, J. Math. Kyoto Univ. 21 (1981), no. 4, 839-859. · Zbl 0499.76061
[12] M. Umehara and A. Tani, Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas, J. Differential Equations 234 (2007), no. 2, 439-463. · Zbl 1119.35070 · doi:10.1016/j.jde.2006.09.023
[13] M. Umehara and A. Tani, Temporally global solution to the equations for a spherically symmetric viscous radiative and reactive gas over the rigid core, Anal. Appl. 6 (2008), 183-211. · Zbl 1151.35107 · doi:10.1142/S0219530508001122
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.