# 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)
On the Stokes equations: The boundary value problem. (English) Zbl 0949.35111
Maremonti, Paolo (ed.), Advances in fluid dynamics. Rome: Aracne. Quad. Mat. 4, 69-140 (1999).

This paper deals with a boundary value problem (bvp) for the Stokes equation. The corresponding domain ${\Omega }$ is not obliged to be simply connected and it can be either a bounded or an exterior one. In their investigations the authors use the theory of hydrodynamical potentials. An existence of a unique classical solution is proved in the case of a bounded domain ${\Omega }$ (§5). Similar results are obtained in §6, §7 assuming ${\Omega }$ to be an exterior domain. To be more precise, we give the uniqueness result as follows: Let $\left({u}_{1},{p}_{1}\right)$, $\left({u}_{2},{p}_{2}\right)$ be two classical solutions of the Stokes bvp. Then, if

${u}_{1}-{u}_{2}=\left\{\begin{array}{cc}o\left(logr\right),\phantom{\rule{1.em}{0ex}}\hfill & n=2,\hfill \\ o\left(1\right),\phantom{\rule{1.em}{0ex}}\hfill & n\ge 3,\hfill \end{array}\right\$

we have ${u}_{1}={u}_{2}$ and ${p}_{1}={p}_{2}+\text{const}$.

##### MSC:
 35Q30 Stokes and Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory 76D07 Stokes and related (Oseen, etc.) flows