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)
Attractors for nonautonomous nonhomogeneous Navier-Stokes equations. (English) Zbl 0908.35098

The Navier-Stokes equations are considered in a smooth bounded domain Ω 2

u t-νΔu+(u·)u+p=f,divu=0inΩ,u=φonΩ,

where f(x,t) and φ(x,t) are quasiperiodic in t. It means that f(·,t)=f(·,α 1 t,,α k t), φ(·,t)=φ(·,α 1 t,,α k t), where f(·,ω 1 ,,ω k ) and φ(·,ω 1 ,,ω k ) are 2π-periodic in each argument ω i , the {α i } being rationally independent. The authors construct the family of processes associated to these equations and prove the existence of the uniform attractor. The following estimate of the Hausdorff dimension of the attractor 𝒜 k is obtained

dim𝒜 k k+c(G 1 +Re 3/2 )+c ' (G 1 +G 2 +Re 3/2 )k 1/2

where G 1 and G 2 depend of f,φ and Ω, Re is the Reynolds number, c and c ' are nondimensional constants independent of Re,G 1 ,G 2 . The approach of V. V. Chepyzhov and M. I. Vishik [|J. Math. Pures Appl. 73, 279-333 (1994; Zbl 0838.58021)] is used.

MSC:
35Q30Stokes and Navier-Stokes equations
37C70Attractors and repellers, topological structure
76D05Navier-Stokes equations (fluid dynamics)
35-99Partial differential equations (PDE) (MSC2000)