Abstract
We establish an existence theorem for weak solutions of the boundary-value problem for steady-state equations describing both laminar and turbulent flows of nonlinear-viscous fluids.
Similar content being viewed by others
REFERENCES
L. D. Landau and E. M. Lifshits, Hydrodynamics [in Russian], vol. 6, Series “Theoretical Physics,” Nauka, Moscow, 1986.
W. G. Litvinov, “Some models and problems for laminar and turbulent flows of viscous and nonlinear viscous fluids,” J. Math. Phys. Sci., 30 (1996), no. 3, 101-157.
V. T. Dmitrienko and V. G. Zvyagin, “Topological degree method in the equations of the Navier-Stokes type,” Abstract and Applied Analysis, 1-2 (1997), 1-45.
M. A. Krasnosel'skii, Topological Methods in Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow, 1956.
J. Appell and P. P. Zabrejko, Nonlinear Superposition Operators, Cambridge Univ. Press, 1990.
H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordi.erentialgleichungen, Akademie Verlag, Berlin, 1974.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dmitrienko, V.T., Zvyagin, V.G. Solvability of the Boundary-Value Problem for a Mathematical Model of Steady-State Flows of Nonlinear-Viscous Fluids. Mathematical Notes 69, 770–779 (2001). https://doi.org/10.1023/A:1010226330684
Issue Date:
DOI: https://doi.org/10.1023/A:1010226330684