Abstract
The equations of motion of compressible viscous and heat-conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region. The global solution in time is proved to exist uniquely and approach the stationary state ast→∞, provided the prescribed initial data and the external force are sufficiently small.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math.17, 35–92 (1964)
Cattabriga, L.: Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Mat. Sem. Univ. Padova31, 308–340 (1961)
Finn, R.: On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems. Arch. Rat. Mech. Anal.19, 363–406 (1965)
Heywood, J. G.: A uniqueness theorem for non-stationary Navier-Stokes flow past an obstacle. Ann. Scuola Norm. Sup. Pisa IV6, 427–445 (1979)
Ladyzhenskaya, O. A.: The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1969
Matsumura, A.: An energy method for the equations of motion of compressible viscous and heat-conductive fluids, Univ. of Wisconsin-Madison, MRC Technical Summary Report 2194, 1981
Matsumura, A., Nishida, T.: The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids. Proc. Jpn. Acad. Ser. A,55, 337–342 (1979)
Matsumura, A., Nishida, T.: Initial boundary value problems for the equations of motion of general fluids. Computing Methods in Applied Sciences and Engineering, V, ed. by Glowinski, R., Lions, F. L. North-Holland Publ. Comp. Amsterdam, 1982, 389–406. In: Proc. of 5th Internat. Symp. on Computing Methods in Appl. Sci. and Engin, Dec. 1982, INRIA, Versalities, France
Solonnikov, V. A.:A priori estimates for certain boundary value problems. Sov. Math. Dokl.2, 723 (1961)
Tani, A.: On the first initial-boundary value problem of compressible viscous fluid motion. Publ. RIMS. Kyoto Univ.13, 193–253 (1977)
Author information
Authors and Affiliations
Additional information
Communicated by J. Glimm
Both authors are partially supported by the University of Wisconsin-Madison, Mathematics Research Center
Rights and permissions
About this article
Cite this article
Matsumura, A., Nishida, T. Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Commun.Math. Phys. 89, 445–464 (1983). https://doi.org/10.1007/BF01214738
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01214738