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)
The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. (English) Zbl 1026.76004
Summary: We study the equations governing the motion of second-grade fluids in a bounded domain of $\bbfR^d$, $d=2,3$, with Navier-slip boundary conditions with and without viscosity (averaged Euler equations). We show global existence and uniqueness of $H^3$ solutions in dimension two. In dimension three, we obtan local existence of $H^3$ solutions for arbitrary initial data, and global existence for small initial data and positive viscosity. We close by finding Lyapunov stability conditions for stationary solutions for averaged Euler equations similar to Rayleigh-Arnold stability result for the classical Euler equations.

76A05Non-Newtonian fluids
35Q35PDEs in connection with fluid mechanics
Full Text: DOI