References
L. I. Sedov, Continuum Mechanics. Vol. 1 [in Russian], Nauka, Moscow (1970).
A. Matsumura and T. Nishida, “The initial value problem for the equations of motion of viscous and heat-conductive gases,” J. Math. Kyoto Univ.,20, No. 1, 67–104 (1980).
V. A. Solonnikov, “On solvability of initial-boundary value problems for the equations of motion of a viscous compressible fluid,” in: Studies in Linear Operators and Function Theory [in Russian], Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),56, 128–142 (1976).
A. V. Kazhikhov and V. V. Shelukhin, “Global unique solvability in time of initial-boundary value problems for one-dimensional equations of a viscous gas,” Prikl. Mat. Mekh.,41, 282–291 (1977).
C. Bernardi and O. Pironneau, “On the shallow water equation at low Reynolds numbers,” Comm. Partial Differential Equations,16, No. 1, 59–104 (1991).
A. V. Kazhikhov, “The equation of potential flows of a compressible viscous fluid at small Reynolds numbers: existence, uniqueness, and stabilization of solutions,” Sibirsk. Mat. Zh.,34, No. 3, 70–80 (1993).
L. V. Ovsyannikov, Lectures on the Fundamentals of Gas Dynamics [in Russian], Nauka, Moscow (1981).
V. I. Yudovich, The Linearization Method in Hydrodynamic Stability Theory [in Russian], Rostov. Univ., Rostov-on-Don (1984).
V. I. Yudovich, “A two-dimensional nonstationary flowing problem for an ideal incompressible fluid through a given domain,” Mat. Sb.,64, No. 4, 562–588 (1964).
T. Kato, “On classical solutions of the two-dimensional non-stationary Euler equation,” Arch. Rational Mech. Anal.,25, No. 3, 188–200 (1967).
M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).
Author information
Authors and Affiliations
Additional information
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 37, No. 5, pp. 1117–1131, September–October, 1996.
In conclusion, the author expresses his gratitude to A. V. Kazhikhov for the statement of the problem and interest in the topic.
Rights and permissions
About this article
Cite this article
Mamontov, A.E. Well-posedness of a quasistationary model of a viscous compressible fluid. Sib Math J 37, 983–996 (1996). https://doi.org/10.1007/BF02110728
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110728