On the Cauchy problem associated with the motion of a Bingham fluid in the plane

Kim, Jong Uhn

doi:10.1090/S0002-9947-1986-0857449-X

On the Cauchy problem associated with the motion of a Bingham fluid in the plane
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Trans. Amer. Math. Soc. 298 (1986), 371-400 Request permission

Abstract:

This paper discusses an initial value problem for the variational inequality which describes the motion of a Bingham fluid in the plane. The existence of strong solution is established.

References

G. Duvaut and J.-L. Lions, Inequalities in mechanics and physics, Grundlehren der Mathematischen Wissenschaften, vol. 219, Springer-Verlag, Berlin-New York, 1976. Translated from the French by C. W. John. MR 0521262
Ciprian Foiaş, Colette Guillopé, and Roger Temam, New a priori estimates for Navier-Stokes equations in dimension $3$, Comm. Partial Differential Equations 6 (1981), no. 3, 329–359. MR 607552, DOI 10.1080/03605308108820180
Avner Friedman, Partial differential equations, Corrected reprint of the original edition, Robert E. Krieger Publishing Co., Huntington, N.Y., 1976. MR 0454266
Tosio Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., Vol. 448, Springer, Berlin, 1975, pp. 25–70. MR 0407477
J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969 (French). MR 0259693
Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
Roger Temam, Navier-Stokes equations, Revised edition, Studies in Mathematics and its Applications, vol. 2, North-Holland Publishing Co., Amsterdam-New York, 1979. Theory and numerical analysis; With an appendix by F. Thomasset. MR 603444
Roger Temam, Navier-Stokes equations and nonlinear functional analysis, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 41, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1983. MR 764933
Michael Renardy, Dense imbedding of test functions in certain function spaces, Trans. Amer. Math. Soc. 298 (1986), no. 1, 241–243. MR 857442, DOI 10.1090/S0002-9947-1986-0857442-7