Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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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DOI: https://doi.org/10.1090/qam/1753406
Article copyright: © Copyright 2000 American Mathematical Society


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