## Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids.(English)Zbl 0543.76099

Summary: 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 as $$t\to \infty$$, provided the prescribed initial data and the external force are sufficiently small.

### MSC:

 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Full Text:

### References:

 [1] 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) · Zbl 0123.28706 [2] Cattabriga, L.: Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Mat. Sem. Univ. Padova31, 308-340 (1961) · Zbl 0116.18002 [3] Finn, R.: On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems. Arch. Rat. Mech. Anal.19, 363-406 (1965) · Zbl 0149.44606 [4] Heywood, J. G.: A uniqueness theorem for non-stationary Navier-Stokes flow past an obstacle. Ann. Scuola Norm. Sup. Pisa IV6, 427-445 (1979) · Zbl 0437.76032 [5] Ladyzhenskaya, O. A.: The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1969 · Zbl 0184.52603 [6] 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 [7] 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) · Zbl 0447.76053 [8] 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 [9] Solonnikov, V. A.:A priori estimates for certain boundary value problems. Sov. Math. Dokl.2, 723 (1961) · Zbl 0104.32304 [10] Tani, A.: On the first initial-boundary value problem of compressible viscous fluid motion. Publ. RIMS. Kyoto Univ.13, 193-253 (1977) · Zbl 0366.35070
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.