On the Navier-Stokes equations for exothermically reacting compressible fluids

Acta Mathematicae Applicatae Sinica

Volumn 18, Issue 1, 2002, Pages 169-176

  Chen, Gui Qiang ^a   Hoff, David ^b   Trivisa, Konstantina ^c  

^a NORTHWESTERN UNIVERSITY   (United States)

^b INDIANA UNIVERSITY   (United States)

^c Bldg 142   (United States)

Author keywords

Asymptotic behavior; Combustion; Difference approximations; Discontinuous initial data; Energy estimates; Evolution of large jump discontinuities; Global discontinuous solutions; Large oscillation; Navier Stokes equations; Total variation estimates

Indexed keywords

EID: 2942553528     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s102550200015     Document Type: Article

References (19)

1. Amosov, A.A., Zlotnick, A.A. A Semidiscrete Method for Solving Equations of the One-dimensional Motion of a Non-homogeneous Viscous Heat-conducting Gas with Nonsmooth Data. Izv. Vyssh. Uchebn. Zaved. Mat., 1997, 3-19 (in Russian);
2. Transl. In Russian Math. (Iz. Vuz), 1997, 41: 1-17
3. Amosov, A.A., Zlotnick, A.A. On Stability of Generalized Solutions to the Equations of One-dimensional Motion of a Viscous Heat Conducting Gas. Siberian Math. J., 1997, 38(4): 663-684
4. Chen, G.-Q. Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture. SIAM J. Math. Anal., 1992, 23: 609-634
5. Chen, G.-Q., Hoff, D., Trivisa, K. Global Solutions of the Compressible Navier-Stokes Equations with Large Discontinuous Initial Data. Commun. Partial Diff. Eqs., 2000, 25: 2233-2257
6. Chen, G.-Q., Hoff, D., Trivisa, K. Global Solutions to the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids with Large Discontinuous Initial Data. Preprint, Northwestern University, 2001
7. Chen, G.-Q., Wagner, D. Global Entropy Solutions to Exothermically Reacting, Compressible Euler Equations. J. Diff. Eqs., (to Appear)
8. Courant, R., Friedrichs, K.O. Supersonic Flow and Shock Waves. Interscience, New York, 1948
9. Dafermos, C.M. Global Smooth Solutions to the Initial-Boundary Value Problem for the Equations of One-dimensional Nonlinear Thermoviscoelasticity. SIAM J. Math. Anal., 1982, 13: 397-408
10. Glimm, J. The Continuous Structure of Discontinuities. Lecture Notes In Physics, 1989, 344: 177-186
11. Godlewski, E., Raviart, P. Numerical Approximation of Hyperbolic Systems Of Conservation Laws. Appl. Math. Sc., Vol.118, Springer-Verlag, New York, 1996
12. Hoff, D. Global Well-posedness of the Cauchy Problem for Nonisentropic Gas Dynamics with Discontinuous Initial Data. J. Diff. Eqs., 1992, 95: 33-74
13. Hoff, D. Discontinuous Solutions of the Navier-Stokes Equations for Compressible Flow. Arch. Rational Mech. Anal., 1991, 114: 15-46
14. Hoff, D. Discontinuous Solutions of the Navier-Stokes Equations for Multidimensional Heat-conducting Fluids. Arch. Rational Mech. Anal., 1997, 139: 303-354
15. Hoff, D., Serre, D. The Failure of Continuous Dependence on the Initial Data for the Navier-Stokes Equations of Compressible Flow. SIAM J. Appl. Math., 1991, 51: 887-898
16. Kanel, Y. On a Model System of Equations of One-dimensional Gas Motion. J. Diff. Eq., 1968, 4: 374-380
17. Kazhikhov, A.V. On the Theory of Initial-boundary-value Problems for the Equations of One-dimensional Nonstationary Motion of a Viscous Heat-conductive Gas. Din. Sploshnoi Sredy, 1981, 50: 37-62 (in Russian)
18. 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
19. Matsumura, A., Yanagi, S. Uniform Boundedness of the Solutions for a One-dimensional Isentropic Model System of Compressible Viscous Gas. Commun. Math. Phys., 1996, 175: 259-274