zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids. (English) Zbl 0904.76006
Summary: Three-dimensional, unsteady, laminar boundary layer equations of a general model of non-Newtonian fluids are treated. In this model, the shear stresses are considered to be arbitrary functions of velocity gradients. Using Lie group analysis, we calculate the infinitesimal generators accepted by the equations in the arbitrary shear stress case. The extension of Lie algebra, for the case of Newtonian fluids, is also presented. Then we consider a general boundary value problem modeling the flow over a moving surface with suction or injection, and calculate the restrictions imposed by the boundary conditions on the generators. Assuming all flow quantities to be independent of the z-direction, the three-independent-variable partial differential system is converted into a two-independent-variable system by using two different subgroups of the general group. Lie group analysis is further applied to the resulting equations, and final reductions to ordinary differential systems are obtained.
76A05Non-Newtonian fluids
35Q35PDEs in connection with fluid mechanics
35A30Geometric theory for PDE, characteristics, transformations