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)
Long waves on a thin layer of conducting fluid flowing down an inclined plane in an electromagnetic field. (English) Zbl 0934.76097
Summary: We study the propagation of weakly nonlinear waves over a flow of an electrically conducting viscous film flowing down an inclined plane under simultaneous action of electrical and magnetic fields. The Navier-Stokes equations with electromagnetic force in the limit of low magnetic Reynolds number and subject to corresponding boundary conditions serve as a mathematical description of the problem. Long-wave expansions are carried out, and an evolution equation of the Kuramoto-Sivashinsky type governing propagation of weak surface perturbations is derived. The critical values of the Reynolds number are determined explicitly, and linear stability is investigated. We show that the electrical field has a destabilizing effect on the film flow, while the magnetic field stabilizers it. The strongest stabilizing effect of the magnetic field in the presence of electrical one can be achieved if the magnetic field is purely longitudinal. We also consider the application of the Kármán-Pohlhausen integral boundary-layer theory.
MSC:
76W05Magnetohydrodynamics and electrohydrodynamics
76E25Stability and instability of magnetohydrodynamic and electrohydrodynamic flows