Existence and regularity of solutions of non-Newtonian flow
Author:
Hyeong-Ohk Bae
Journal:
Quart. Appl. Math. 58 (2000), 379-400
MSC:
Primary 76A05; Secondary 35Q35, 76D03
DOI:
https://doi.org/10.1090/qam/1753406
MathSciNet review:
MR1753406
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Abstract: The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonian flows are considered. Galerkin approximation and an ${L^{2}}$ compactness theorem are main ingredients for the proof of the existence of Young measure-valued solutions. Under a certain convexity condition for the energy, we prove that Young measure-valued solutions are weak solutions. Also, for the limited cases, we prove a regularity theorem.
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H. Bellout, F. Bloom, and J. Nečas, Young measure-valued solutions for non-Newtonian incompressible fluids, Comm. Partial Differential Equations 19, 1763–1803 (1994)
H. Bellout, F. Bloom, and J. Nečas, Existence, uniqueness, and stability of solutions to the initial boundary value problem for bipolar viscous fluid, Differential and Integral Equations 8, 453–464 (1995)
G. Böhme, Non-Newtonian Fluid Mechanics, North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publishing Co., Amsterdam, 1987
C. Foiaş, C. Guillopé, and R. Temam, New a priori estimates for Navier-Stokes equations in dimension 3, Comm. Partial Differential Equations 6, 329–359 (1981)
O. A. Ladyzhenskaya, New equations for the description of the viscous incompressible fluids and solvability in the large of the boundary value problems for them, Boundary Value Problems of Mathematical Physics V, Amer. Math. Soc., Providence, RI, 1970
J. Málek and J. Nečas, A finite-dimensional attractor for three-dimensional flow of incompressible fluids, J. Differential Equations 127, 498–518 (1996)
P. P. Mosolov and V. P. Mjasnikov, A proof of Korn’s inequality, Soviet Math. Dokl. 12, 1618–1622 (1971)
J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elasto-plastic Bodies: An Introduction, Elsevier Scientific Publishing Co., Amsterdam and New York, 1980
R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, Studies in Mathematics and its Applications, Vol. 2, North-Holland Publishing Co., Amsterdam, New York, Oxford, 1977
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American Mathematical Society
