About: Ladyzhenskaya's inequality

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In mathematics, Ladyzhenskaya's inequality is any of a number of related functional inequalities named after the Soviet Russian mathematician Olga Aleksandrovna Ladyzhenskaya. The original such inequality, for functions of two real variables, was introduced by Ladyzhenskaya in 1958 to prove the existence and uniqueness of long-time solutions to the Navier–Stokes equations in two spatial dimensions (for smooth enough initial data). There is an analogous inequality for functions of three real variables, but the exponents are slightly different; much of the difficulty in establishing existence and uniqueness of solutions to the three-dimensional Navier–Stokes equations stems from these different exponents. Ladyzhenskaya's inequality is one member of a broad class of inequalities known as inte

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rdfs:label	Ladyzhenskaya's inequality (en)
rdfs:comment	In mathematics, Ladyzhenskaya's inequality is any of a number of related functional inequalities named after the Soviet Russian mathematician Olga Aleksandrovna Ladyzhenskaya. The original such inequality, for functions of two real variables, was introduced by Ladyzhenskaya in 1958 to prove the existence and uniqueness of long-time solutions to the Navier–Stokes equations in two spatial dimensions (for smooth enough initial data). There is an analogous inequality for functions of three real variables, but the exponents are slightly different; much of the difficulty in establishing existence and uniqueness of solutions to the three-dimensional Navier–Stokes equations stems from these different exponents. Ladyzhenskaya's inequality is one member of a broad class of inequalities known as inte (en)
dcterms:subject	Sobolev spaces Inequalities Fluid dynamics
Wikipage page ID	38489856 (xsd:integer)
Wikipage revision ID	1117757656 (xsd:integer)
Link from a Wikipage to another Wikipage	Interpolation inequality Compactly supported Mathematics Russians Lp space Sobolev spaces Smooth function Sobolev space Soviet people Mathematician Agmon's inequality Gagliardo–Nirenberg interpolation inequality Lipschitz domain Inequalities Fluid dynamics Trace operator Navier–Stokes equations Weak derivative Olga Aleksandrovna Ladyzhenskaya
sameAs	Ladyzhenskaya's inequality Ladyzhenskaya's inequality Ladyzhenskaya's inequality Ladyzhenskaya's inequality
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has abstract	In mathematics, Ladyzhenskaya's inequality is any of a number of related functional inequalities named after the Soviet Russian mathematician Olga Aleksandrovna Ladyzhenskaya. The original such inequality, for functions of two real variables, was introduced by Ladyzhenskaya in 1958 to prove the existence and uniqueness of long-time solutions to the Navier–Stokes equations in two spatial dimensions (for smooth enough initial data). There is an analogous inequality for functions of three real variables, but the exponents are slightly different; much of the difficulty in establishing existence and uniqueness of solutions to the three-dimensional Navier–Stokes equations stems from these different exponents. Ladyzhenskaya's inequality is one member of a broad class of inequalities known as interpolation inequalities. Let be a Lipschitz domain in for and let be a weakly differentiable function that vanishes on the boundary of in the sense of trace (that is, is a limit in the Sobolev space of a sequence of smooth functions that are compactly supported in ). Then there exists a constant depending only on such that, in the case : and in the case : (en)
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page length (characters) of wiki page	4806 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ladyzhenskaya's_inequality
is Link from a Wikipage to another Wikipage of	Interpolation inequality List of inequalities Gagliardo–Nirenberg interpolation inequality Olga Ladyzhenskaya Ladyzhenskaya inequality
is Wikipage redirect of	Ladyzhenskaya inequality
is known for of	Olga Ladyzhenskaya
is known for of	Olga Ladyzhenskaya
is foaf:primaryTopic of	wikipedia-en:Ladyzhenskaya's_inequality

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