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)
Well-posedness for the Navier slip thin-film equation in the case of partial wetting. (English) Zbl 1227.35146
The author addresses well-posedness and regularity for the Navier slip thin-film equation in the case of partial wetting. As many people know that if one considers a viscous liquid droplet spreading on a surface, the classical boundary condition for the Navier-Stokes equations at a liquid-solid interface is the no-slip condition. However, if a no-slip condition is imposed, then any movement of the contact line leads to infinite dissipation of energy at the moving contact line. For this reason, other slip conditions such as the Navier slip condition have been proposed. The author proves well-posedness for a reduced 1-D fluid model related to Navier slip. It turns out that the profile of the droplet cannot be described by a smooth function. By using some methods such as a fixed point argument, the theories on weighted Sobolev spaces, the Laplace transformation etc., the author also addresses the existence, uniqueness and regularity of the problem.

35K25Higher order parabolic equations, general
35B65Smoothness and regularity of solutions of PDE
35A01Existence problems for PDE: global existence, local existence, non-existence
76A20Thin fluid films (fluid mechanics)
35Q35PDEs in connection with fluid mechanics
Full Text: DOI