Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-29T13:41:43.316Z Has data issue: false hasContentIssue false

The equations of viscous incompressible non-homogeneous fluids: on the existence and regularity

Published online by Cambridge University Press:  17 February 2009

Rodolfo Salvi
Affiliation:
Dipartimento di Mathematica, Politecnico di Milano, Italy.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the existence and regularity of the solution of an initial boundary value problem for viscous incompressible non-homogeneous fluids, using a semi-Galerkin approximation and so-called compatibility conditions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Cattabriga, L., “Su un problema al contorno relativo al sistema di equazioni di Stokes”, Rend. Mat. Sent. Univ. Padova 31 (1961) 308340.Google Scholar
[2]Heywood, J. G., “The Navier-Stokes equations: On the existence, regularity and decay of solutions”, Indiana Univ. Math. J. 29 (1980) 639681.CrossRefGoogle Scholar
[3]Heywood, J. G. and Rannacher, R., “Finite element approximation of the non-stationary Navier-Stokes problem I”, Siam J. Numer. Anal. 19 (1982) 275311.CrossRefGoogle Scholar
[4]Kajikhov, V. A., “Resolution of boundary value problems for non-homogeneous viscous fluids”, Dok Akad. Nauk. 216 (1974) 10081010.Google Scholar
[5]Kim, J. V., “Weak solutions of an initial boundary-value for an incompressible viscous fluid with non-negative density”, Siam J. Math. Anal. 18 (1987) 8996.CrossRefGoogle Scholar
[6]Ladyzhenskaya, O. A. and Solonnikov, V. A., “Unique solvability of an initial and boundary value problem for viscous incompressible non-homogeneous fluids”, J. Sov. Math. 9 (1978) 697749.CrossRefGoogle Scholar
[7]Lions, J. L., “Quelques methodes de resolution des problems aux limites non-lineares”, Dunod Gauthier-Villars, Paris, 1969.Google Scholar
[8]Rautmann, R., “Optimum regularity of Navier-Stokes solutions at time t = 0”, Math. Z. 184 (1983) 141149.CrossRefGoogle Scholar
[9]Salvi, R., “Error estimates for the spectral Galerkin approximations of the solutions of Navier-Stokes type equations”, Glasgow Math. J. 31 (1989) 199211.CrossRefGoogle Scholar
[10]Simon, J., “Ecoulemend d'un fluide non-homogene avec densite initiate s'annulant”, C. R. Acad. Sci. 287 (1978) 11091112.Google Scholar
[11]Temam, R., “Behaviour at time t = 0 of the solutions of semi-linear evolution equations”, J. Differential Equations, 43 (1982) 7392.CrossRefGoogle Scholar
[12]Temam, R., “Navier-Stokes equations and non-linear functional analysis”. Society for Industrial and Applied Mathematics, 1983.Google Scholar