Discontinuous solutions of the navier-stokes equations for multidimensional flows of heat-conducting fluids

Archive for Rational Mechanics and Analysis

Volumn 139, Issue 4, 1997, Pages 303-354

  Hoff, David ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; DENSITY OF LIQUIDS; FLOW OF FLUIDS; HEAT CONDUCTION; PRESSURE; TEMPERATURE; VELOCITY; VORTEX FLOW;

HEAT CONDUCTING FLUIDS; MULTIDIMENSIONAL FLOW;

NAVIER STOKES EQUATIONS;

EID: 0031240677     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050055     Document Type: Article

References (20)

1. G. K. BATCHELOR, An Introduction to Fluid Dynamics, Cambridge Univ. Press, 1967.
2. R. J. DiPerna & P. L. LIONS, Ordinary differential equations, transport theory, and Sobolev spaces, Inventiones Mathematicae 98 (1989), 511-547.
3. W. F. DONOGHUE, JR., Distributions and Fourier Transforms, Academic Press, 1969.
4. P. DUHEM, Recherches sur l'hydrodynamiques, Ann. Toulouse 2 (1901-02).
5. D. HOFF, Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data, Proc. Royal Soc. Edinburgh, A103 (1986), 301-315.
6. D. HOFF, Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data, Trans. Amer. Math. Soc. 303 (1987), 169-181.
7. D. HOFF, Global well-posedness of the Cauchy problem for nonisentropic gas dynamics with discontinuous initial data, J. Diff. Eq. 95 (1992), 33-73.
8. D. HOFF, Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data, Indiana Univ. Math. J. 41 (1992), 1225-1302.
9. D. HOFF, Global solutions of the Navier-Stokes equations for multidimensonal compressible flow with discontinuous initial data, J. Diff. Eqs. 120 (1995), 215-254.
10. D. HOFF, Strong convergence to global solutions for compressible, viscous, multidimensional flow, with polytropic equations of state and discontinuous initial data, Arch. Rational Mech. Anal. 132 (1995), 1-14.
11. S. KAWASHIMA, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Ph. D. Thesis. Kyoto University, 1983.
12. P.-L. LIONS, Existence globale de solutions pour les équations de Navier-Stokes compressibles isentropiques, C.R. Acad. Sci. Paris 316 (1993), 1335-1340.
13. A. MATSUMURA & TAKAAKI NISHIDA, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104.
14. R. RACKE, Lectures on Nonlinear Evolution Equations, Vieweg Verlag, 1992.
15. D. SERRE, Sur l'équation monodimensionnelle d'un fluide visqueux, compressible et conducteur de chaleur, C.R. Acad. Sc. Paris 303 (1986), 703-706.
16. D. SERRE, Variations de grande amplitude pour la densité d'un fluide visqueux compressible, Physics D 48 (1991), 113-128.
17. J. SERRIN, Mathematical principles of classical fluid mechanics, in Handbuch der Physik VIII, Springer-Verlag, 1959.
18. V.V. SHELUKHIN, On the structure of generalized solutions of the one-dimensional equations of a polytropic viscous gas, Prikl. Mat. Mekh. 48 (1984), 912-920.
19. E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
20. W. ZIEMER, Weakly Differentiable Functions, Springer-Verlag, 1989.