Existence of the unique strong solution for a class of non-Newtonian fluids with vacuum
Authors:
Xiaojing Xu and Hongjun Yuan
Journal:
Quart. Appl. Math. 66 (2008), 249-279
MSC (2000):
Primary 76A05, 76N10
DOI:
https://doi.org/10.1090/S0033-569X-08-01103-9
Published electronically:
February 8, 2008
MathSciNet review:
2416773
Full-text PDF Free Access
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Additional Information
Abstract: The aims of this paper are to discuss local existence and uniqueness of solutions for a class of non-Newtonian fluids with vacuum in one-dimensional bounded intervals. The important point in this paper is that we allow the initial vacuum.
References
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References
- 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, in “Boundary Value Problems of Mathematical Physics V”, Amer. Math. Soc., Providence, RI, 1970.
- S. Whitaker, “Introduction to fluid mechanics”, Krieger, Melbourne, FL, 1986.
- J. Nečas, M. Šilhavý, Multipolar viscous fluids, Quarterly of Applied Mathematics, 1991, Vol.XLIX(2), 247-265. MR 1106391 (92d:76005)
- H. Bellout, F. Bloom, J. Nečas, Phenomenological behavior of multipolar viscous fluids, Quarterly of Applied Mathematics, 1992, Vol.L(3), 559-583. MR 1178435 (93g:76006)
- J. Málek, J. Nečas, M. Rokyta, M. Ru̇žička, Weak and Measure-valued Solutions to Evolutionary PDEs, Chapman and Hall, New York, 1996. MR 1409366 (97g:35002)
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- J. Nečas, A. Novotný, M. Šilhavý, Global solution to the compressible isothermal multipolar fluid, Journal of Mathematical Analysis and Applications, 1991, Vol.162, 223-241. MR 1135273 (93e:35089)
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Additional Information
Xiaojing Xu
Affiliation:
Sch. Math. Sci. & Lab. Math. Com. Sys., Beijing Normal University, Beijing, 100875, China, and Institute of Mathematics, Jilin University, Changchun, Jilin, 130012, China
Email:
xjxu@bnu.edu.cn
Hongjun Yuan
Affiliation:
Institute of Mathematics, Jilin University, Changchun, Jilin, 130012, China
Email:
hjy@jlu.edu.cn
Keywords:
Existence and uniqueness,
non-Newtonian fluid,
vacuum
Received by editor(s):
May 16, 2006
Published electronically:
February 8, 2008
Additional Notes:
Supported by program 985 of Jilin University; China Postdoctoral Sciences Foundation; NSF Grants [10571072] and [10601009]; Program 973 [2006cb805900]
Article copyright:
© Copyright 2008
Brown University
The copyright for this article reverts to public domain 28 years after publication.