Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-05T08:23:25.908Z Has data issue: false hasContentIssue false

Variational inequalities of Bingham type in three dimensions

Published online by Cambridge University Press:  22 January 2016

Yoshio Kato*
Affiliation:
Department of Applied Physics, School of Engineering, Nagoya University, Nagoya 464-01, Japan
Rights & Permissions [Opens in a new window]

Extract

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.

The flow of Bingham type through a domain Ω in the d-th dimensional space Rd (d ≥ 2) during the time (0, T) is a flow of an incompressible visco-plastic fluid governed by the equations for a velocity vector u = (u1,…,ud) and a stress tensor

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] Astarita, G. and Marrucci, G., Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, 1974.Google Scholar
[2] Berger, M. S., Nonlinear and Functional Analysis, Academic Press, New York-San Francisco-London, 1977.Google Scholar
[3] Brezis, H., Problèmes unilateraux, J. Math. Pures Appl., 51 (1972), 1168.Google Scholar
[4] Cattabriga, L., Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Mat. Univ. Padova, 31 (1961), 308340.Google Scholar
[5] Duvaut, G. and Lions, J. L., Ecoulement d’un fluide rigide viscoplastique incompressible, C. R. Acad. Sc. Paris, 270 (1970), 5861.Google Scholar
[6] Duvaut, G. and Lions, J. L., Les inéquations en méchanique et en physique (English translation), Springer-Verlag, Berlin-Heiderberg-New York, 1976.Google Scholar
[7] Kim, J. U., On the Cauchy problem associated with the motion of a Bingham fluid in the plane, Trans. Amer. Math. Soc., 298 (1986), 371400.Google Scholar
[8] Kim, J. U., On the initial boundary value problem for a Bingham fluid in a three dimensional domain, Trans. Amer. Math. Soc., 304 (1987), 751770.Google Scholar
[9] Lions, J. L., Quelque méthodes de résolution des problèmes aux limites non linéaires, Dunod/Gauthier-Villars, Paris, 1969.Google Scholar
[10] Masuda, K., Weak solutions of Navier-Stokes equations, Tôhoku Math. J., 36 (1984), 623646.Google Scholar
[11] Miyakawa, T. and Sohr, H., On energy inequality, smoothness and large time behavior in L 2 for weak solutions of the Navier-Stokes equations in exterior domains, Math. Z., 199 (1988), 455478.Google Scholar
[12] Mosolov, P. P. and Mjasnikov, V. P., On the correctness of boundary value problems in the mechanics of continuous media, Math. USSR Sbornik, 17 (1972), 257268.Google Scholar
[13] Naumann, J. and Wulst, , On evolution inequalities of Bingham type in three dimensions, I, J. Math. Anal. Appl., 68 (1979), 211227.CrossRefGoogle Scholar
[14] Naumann, J. and Wulst, , On evolution inequalities of Bingham type in three dimensions, II, J. Math. Anal. Appl., 70 (1979), 309325.Google Scholar
[15] Renardy, M., Dense imbedding of test funtions in certain function spaces, Trans. Amer. Math. Soc., 298 (1986), 241243.Google Scholar
[16] Strauss, M. J., Variations of Korn’s and Sobolev’s inequalities, Berkeley symposium on partial differential equations, A.M.S. Symposia, 23 (1971).Google Scholar
[17] Temam, R., Navier-Stokes equations, North-Holland, 1977.Google Scholar
[18] Yosida, K., Functional Analysis, Springer-Verlag, Berlin-Heiderberg-New York, 1966.Google Scholar