zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces. (English) Zbl 1231.35155
Summary: Solutions for a class of degenerate, nonlinear, nonlocal boundary value problems, arising in nano boundary layer fluid flows over a stretching surface, are obtained. Viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are considered. Using the Schauder fixed point theorem, existence and uniqueness results are established. The effects of the slip parameter k and the suction parameter a on the fluid velocity and on the tangential stress are investigated and discussed (through numerical results). We find that for fluid flows at nanoscales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter k.
MSC:
35Q30Stokes and Navier-Stokes equations
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
35A01Existence problems for PDE: global existence, local existence, non-existence
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness
References:
[1]Navier, C. L. M.H.: Mémoire sur LES lois du mouvement des fluids, Mém. acad. Roy. sci. Inst. France 6, 389 (1823)
[2]Shikhmurzaev, Y. D.: The moving contact line on a smooth solid surface, Int. J. Multiph. flow 19, 589 (1993) · Zbl 1144.76452 · doi:10.1016/0301-9322(93)90090-H
[3]C.H. Choi, J.A. Westin, K.S. Breuer, To slip or not to slipwater flows in hydrophilic and hydrophobic microchannels, in: Proceedings of IMECE 2002, New Orlaneas, LA, Paper No. 2002-33707.
[4]Matthews, M. T.; Hill, J. M.: Nano boundary layer equation with nonlinear Navier boundary condition, J. math. Anal. appl. 333, 381 (2007) · Zbl 1207.76050 · doi:10.1016/j.jmaa.2006.08.047
[5]Wang, C. Y.: Analysis of viscous flows due to a stretching sheet with surface slip and suction, Nonlinear anal. RWA 10, 375 (2009) · Zbl 1154.76330 · doi:10.1016/j.nonrwa.2007.09.013
[6]Van Gorder, R. A.; Sweet, E.; Vajravelu, K.: Nano boundary layers over stretching surfaces, Commun. nonlinear sci. Numer. simul. 15, 1494 (2010) · Zbl 1221.76024 · doi:10.1016/j.cnsns.2009.06.004
[7]Gilbarg, David; Trudinger, Neils S.: Elliptic partial differential equations of second order, Grundlehren der mathematischen wissenschaften 224 (1983) · Zbl 0562.35001
[8]Evans, L.: Partial differential equations: second edition graduate studies in mathematics, (2010)
[9]Vajravelu, K.; Cannon, J. R.: Fluid flow over a nonlinearly stretching sheet, Appl. math. Comput. 181, No. 1, 609-618 (2006) · Zbl 1143.76024 · doi:10.1016/j.amc.2005.08.051
[10]Cortell, R.: Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. math. Comput. 184, No. 2, 864-873 (2007) · Zbl 1112.76022 · doi:10.1016/j.amc.2006.06.077
[11]Crane, L. J.: Flow past a stretching plan, J. appl. Math. phys. (ZAMP) 21, 645-647 (1970)
[12]Wang, C. Y.; Du, G.; Miklavcic, M.; Chang, C. C.: Impulsive stretching of a surface in a viscous fluid, SIAM J. Appl. math. 57, 1-14 (1997) · Zbl 0869.76013 · doi:10.1137/S0036139995282050
[13]Wang, C. Y.: Natural convection on a vertical radially stretching sheet, J. math. Anal. appl. 332, No. 2, 877-883 (2007) · Zbl 1117.35068 · doi:10.1016/j.jmaa.2006.11.006
[14]Sajid, M.; Hayat, T.: The application of the homotopy analysis method for MHD viscous flow due to a shrinking sheet, Chaos solitons fractals 39, 1317-1323 (2009) · Zbl 1197.76100 · doi:10.1016/j.chaos.2007.06.019
[15]Ascher, U.; Mattheij, R.; Russell, R.: Numerical solution of boundary value problems for ordinary differential equations, SIAM classics appl. Math. 13 (1995) · Zbl 0843.65054
[16]Ascher, U.; Petzold, L.: Computer methods for ordinary differential equations and differential–algebraic equations, (1998) · Zbl 0908.65055