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)
Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics. (English) Zbl 1153.76051
Summary: The conservation laws for second-order scalar partial differential equations and systems of partial differential equations which occur in fluid mechanics are constructed using different approaches. The direct method, Noether’s theorem, the characteristic method, the variational approach (multiplier approach) for arbitrary functions as well as on the solution space, symmetry conditions on the conserved quantities, the direct construction formula approach, the partial Noether approach and the Noether approach for the equation and its adjoint are discussed and explained with the help of an illustrative example on a nonlinear field equation describing the relaxation to a Maxwellian distribution. The conservation laws for the nonlinear diffusion equation for the spreading of an axisymmetric thin liquid drop, the system of two partial differential equations governing flow in a laminar two-dimensional jet and the system of two partial differential equations governing flow in a laminar radial jet are discussed via these approaches.
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
76R50Diffusion (fluid mechanics)