Boundary value problems in microcontinuum fluid mechanics
Author:
H. Ramkissoon
Journal:
Quart. Appl. Math. 42 (1984), 129-141
MSC:
Primary 76A05; Secondary 65R20
DOI:
https://doi.org/10.1090/qam/745094
MathSciNet review:
745094
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Abstract: This paper examines the existence and uniqueness of solutions of certain boundary-value problems associated with a seemingly complex system of coupled partial differential equations frequently encountered in the field of microcontinuum fluid mechanics. These problems are analyzed using potential theory methods and appealing to results from the theory of singular integral equations. Matrices are introduced to facilitate this analysis.
- A. Cemal Eringen, Theory of micropolar fluids, J. Math. Mech. 16 (1966), 1–18. MR 0204005, DOI https://doi.org/10.1512/iumj.1967.16.16001
- H. Ramkissoon, On the uniqueness and existence of Stokes flows in micropolar fluid theory, Acta Mech. 35 (1980), no. 3-4, 259–270 (English, with German summary). MR 567334, DOI https://doi.org/10.1007/BF01190401
- H. Ramkissoon and S. R. Majumdar, Representations and fundamental singular solutions in micropolar fluid, Z. Angew. Math. Mech. 56 (1976), no. 5, 197–203 (English, with German and Russian summaries). MR 411347, DOI https://doi.org/10.1002/zamm.19760560505
- S. G. Mikhlin, Multidimensional singular integrals and integral equations, Pergamon Press, Oxford-New York-Paris, 1965. Translated from the Russian by W. J. A. Whyte; Translation edited by I. N. Sneddon. MR 0185399
- G. C. Hsiao and W. L. Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3 (1981), no. 4, 299–315. MR 634453
A. C. Eringen, Theory of micropolar fluids, J. Math. Mech. 16, 1–18 (1966)
H. Ramkissoon, On the uniqueness and existence of Stokes flows in micropolar fluid theory. Acta Mech. 35, 259–270 (1980)
H. Ramkissoon and S. R. Majumdar, Representations and fundamental singular solutions in micropolar fluids, Z. Angew. Math. Mech. 56, 197–203 (1976)
S. G. Mikhlin, Multidimensional singular integrals and integral equations, Pergamon Press (1965)
G. C. Hsiao and W. L. Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3, 299–315 (1981)
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Article copyright:
© Copyright 1984
American Mathematical Society
