Abstract
It is proved that the initial-boundary-value problem for the system of equations describing the motion of a compressible fluid with a constant viscosity is locally solvable with respect to time. The heat conductivity is not taken into account. The solution is found in the class W 2.1 q , q>3.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J. Nash, “Le problème de Cauchy pour les équations différentielles d'un fluide général,” Bull. Soc. Math. France,90, 487–497 (1962).
A. I. Vol'pert and S. I. Khudyaev, “On the Cauchy problem for composite systems of nonlinear differential equations,” Mat. Sb.,87, 504–528 (1972).
O. A. Ladyzhenskaya and V. A. Solonnikov, “On the unique solvability of initial-boundary-value problems for viscous incompressible nonhomogeneous fluids,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,52 (1975).
V. A. Solonnikov, “On boundary-value problems for linear parabolic systems of differential equations of general form,” Tr. Mat. Inst. im. V. S. Steklova Akad. Nauk SSSR,83, 3–162 (1965).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 56, pp. 128–142, 1976.
Rights and permissions
About this article
Cite this article
Solonnikov, V.A. Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid. J Math Sci 14, 1120–1133 (1980). https://doi.org/10.1007/BF01562053
Issue Date:
DOI: https://doi.org/10.1007/BF01562053