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)
A note on the blow-up criterion for the inviscid 2-D Boussinesq equations. (English) Zbl 0991.35070
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 131-140 (2002).
Summary: We show that a smooth solution of the 2-D Boussinesq equations $$\partial_tu+ u\cdot\nabla u+\nabla p=\theta f,\quad \partial_t \theta+ u\cdot \nabla\theta =0,\quad \text{div }u=0,$$ in the whole plane $\bbfR^2$ breaks down if and only if a certain norm of $\nabla\theta$ blows up at the same time. Here the norm is weaker than the $L^\infty$-norm and generates a Banach space including singularities of $\log\log 1/ |x|$. Roughly speaking, when a smooth solution breaks down, $\nabla\theta$ has stronger singularities than $\log\log 1/ |x|$ or has an infinite number of singularities. For the entire collection see [Zbl 0972.00046].

35Q35PDEs in connection with fluid mechanics
35B40Asymptotic behavior of solutions of PDE
76B07Free-surface potential flows