Instability of viscous flows over a shrinking sheet
Author:
M. Miklavčič
Journal:
Quart. Appl. Math. 72 (2014), 363-371
MSC (2010):
Primary 35Q30, 76E09, 35K58, 76D03, 76E25
DOI:
https://doi.org/10.1090/S0033-569X-2013-01340-3
Published electronically:
December 30, 2013
MathSciNet review:
3186242
Full-text PDF Free Access
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Additional Information
Abstract: We prove instability of a part of a branch of viscous incompressible fluid flows induced by a shrinking sheet. These flows are exact solutions of the Navier-Stokes equation.
References
- Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244
- Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin-New York, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147
- T. Kato, Perturbation Theory for Linear Operators, 2nd edition, Springer, New York, 1980.
- Milan Miklavčič, Nonlinear stability of asymptotic suction, Trans. Amer. Math. Soc. 281 (1984), no. 1, 215–231. MR 719667, DOI https://doi.org/10.1090/S0002-9947-1984-0719667-9
- Milan Miklavčič, Applied functional analysis and partial differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1998. MR 1784426
- M. Miklavčič and C. Y. Wang, Viscous flow due to a shrinking sheet, Quart. Appl. Math. 64 (2006), no. 2, 283–290. MR 2243864, DOI https://doi.org/10.1090/S0033-569X-06-01002-5
- C. Y. Wang, Q. Du, M. Miklavčič, and C. C. Chang, Impulsive stretching of a surface in a viscous fluid, SIAM J. Appl. Math. 57 (1997), no. 1, 1–14. MR 1429374, DOI https://doi.org/10.1137/S0036139995282050
References
- Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. MR 610244 (83j:35084)
- Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147 (56 \#7452)
- T. Kato, Perturbation Theory for Linear Operators, 2nd edition, Springer, New York, 1980.
- Milan Miklavčič, Nonlinear stability of asymptotic suction, Trans. Amer. Math. Soc. 281 (1984), no. 1, 215–231. MR 719667 (84m:35098), DOI https://doi.org/10.2307/1999531
- Milan Miklavčič, Applied functional analysis and partial differential equations, World Scientific Publishing Co. Inc., River Edge, NJ, 1998. MR 1784426 (2001k:47001)
- M. Miklavčič and C. Y. Wang, Viscous flow due to a shrinking sheet, Quart. Appl. Math. 64 (2006), no. 2, 283–290. MR 2243864 (2007c:76021)
- C. Y. Wang, Q. Du, M. Miklavčič, and C. C. Chang, Impulsive stretching of a surface in a viscous fluid, SIAM J. Appl. Math. 57 (1997), no. 1, 1–14. MR 1429374 (97k:76032), DOI https://doi.org/10.1137/S0036139995282050
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Additional Information
M. Miklavčič
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
milan@math.msu.edu
Received by editor(s):
August 8, 2012
Published electronically:
December 30, 2013
Article copyright:
© Copyright 2013
Brown University
