Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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

Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • [1] Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. MR 610244 (83j:35084)
  • [2] Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147 (56 #7452)
  • [3] T. Kato, Perturbation Theory for Linear Operators, 2nd edition, Springer, New York, 1980.
  • [4] Milan Miklavčič, Nonlinear stability of asymptotic suction, Trans. Amer. Math. Soc. 281 (1984), no. 1, 215-231. MR 719667 (84m:35098), https://doi.org/10.2307/1999531
  • [5] Milan Miklavčič, Applied functional analysis and partial differential equations, World Scientific Publishing Co. Inc., River Edge, NJ, 1998. MR 1784426 (2001k:47001)
  • [6] 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)
  • [7] 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), https://doi.org/10.1137/S0036139995282050

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 35Q30, 76E09, 35K58, 76D03, 76E25

Retrieve articles in all journals with MSC (2010): 35Q30, 76E09, 35K58, 76D03, 76E25


Additional Information

M. Miklavčič
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: milan@math.msu.edu

DOI: https://doi.org/10.1090/S0033-569X-2013-01340-3
Received by editor(s): August 8, 2012
Published electronically: December 30, 2013
Article copyright: © Copyright 2013 Brown University

American Mathematical Society