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)
Density-dependent incompressible fluids in bounded domains. (English) Zbl 1142.76354

Summary: This paper is devoted to the study of the initial value problem for density dependent incompressible viscous fluids in a bounded domain of N (N2) with C 2+ε boundary. Homogeneous Dirichlet boundary conditions are prescribed on the velocity. Initial data are almost critical in term of regularity: the initial density is in W 1,q for some q>N, and the initial velocity has ϵ fractional derivatives in L r for some r>N and ϵ arbitrarily small. Assuming in addition that the initial density is bounded away from 0, we prove existence and uniqueness on a short time interval. This result is shown to be global in dimension N=2 regardless of the size of the data, or in dimension N3 if the initial velocity is small.

Similar qualitative results were obtained earlier in dimension N=2,3 by O. A. Ladyshenskaya and V. A. Solonnikov [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 52, 52–109 (1975; Zbl 0376.76021)] for initial densities in W 1, and initial velocities in W 2-2 q,q with q>N

76D03Existence, uniqueness, and regularity theory
35Q30Stokes and Navier-Stokes equations
76D05Navier-Stokes equations (fluid dynamics)