On the initial-boundary value problem for a Bingham fluid in a three-dimensional domain
HTML articles powered by AMS MathViewer
- by Jong Uhn Kim PDF
- Trans. Amer. Math. Soc. 304 (1987), 751-770 Request permission
Abstract:
The initial-boundary value problem associated with the motion of a Bingham fluid is considered. The existence and uniqueness of strong solution is proved under a certain assumption on the data. It is also shown that the solution exists globally in time when the data are small and that the solution converges to a periodic solution if the external force is time-periodic.References
- Lamberto Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova 31 (1961), 308–340 (Italian). MR 138894
- Georges Duvaut and Jacques-Louis Lions, Sur de nouveaux problèmes d’inéquations variationnelles posés par la Mécanique. Le cas stationnaire, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A510–A513 (French). MR 261151
- 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, DOI 10.1007/978-3-642-66165-5
- Daisuke Fujiwara, On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators, J. Math. Soc. Japan 21 (1969), 481–522. MR 262682, DOI 10.2969/jmsj/02140481
- Yoshikazu Giga, Analyticity of the semigroup generated by the Stokes operator in $L_{r}$ spaces, Math. Z. 178 (1981), no. 3, 297–329. MR 635201, DOI 10.1007/BF01214869
- Yoshikazu Giga, Domains of fractional powers of the Stokes operator in $L_r$ spaces, Arch. Rational Mech. Anal. 89 (1985), no. 3, 251–265. MR 786549, DOI 10.1007/BF00276874
- Jong Uhn Kim, On the Cauchy problem associated with the motion of a Bingham fluid in the plane, Trans. Amer. Math. Soc. 298 (1986), no. 1, 371–400. MR 857449, DOI 10.1090/S0002-9947-1986-0857449-X
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969 (French). MR 0259693
- J. Naumann and M. Wulst, On evolution inequalities of Bingham type in three dimensions. II, J. Math. Anal. Appl. 70 (1979), no. 2, 309–325. MR 543575, DOI 10.1016/0022-247X(79)90046-5
- 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
- Jacek Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, Państwowe Wydawnictwo Naukowe, Warsaw, 1965. MR 0190409 R. Temam, Navier-Stokes equations, North-Holland, Amsterdam, New York and Oxford, 1984.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 304 (1987), 751-770
- MSC: Primary 35Q10; Secondary 76A99
- DOI: https://doi.org/10.1090/S0002-9947-1987-0911094-7
- MathSciNet review: 911094