Cauchy–Kovalevskaya theorem

E171220

mathematical theorem theorem in partial differential equations

The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.

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All labels observed (4)

Label	Occurrences
Cauchy–Kowalevski theorem	4
Cauchy–Kovalevskaya theorem canonical	2
Cauchy–Kovalevskaya theorem on manifolds	1
Cauchy–Kovalevskaya–Kashiwara theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T1489660 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Cauchy–Kovalevskaya theorem
Context triple: [Sofia Kovalevskaya, notableWork, Cauchy–Kovalevskaya theorem]

A. Peano existence theorem
The Peano existence theorem is a fundamental result in the theory of ordinary differential equations that guarantees the existence (but not necessarily uniqueness) of solutions under mild continuity conditions on the right-hand side.
B. local existence and uniqueness theorem
The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
C. Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
D. Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
E. Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Cauchy–Kovalevskaya theorem
Target entity description: The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.

A. Peano existence theorem
The Peano existence theorem is a fundamental result in the theory of ordinary differential equations that guarantees the existence (but not necessarily uniqueness) of solutions under mild continuity conditions on the right-hand side.
B. local existence and uniqueness theorem
The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
C. Weierstrass preparation theorem
The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
D. Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
E. Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
F. None of above. chosen

Statements (45)

Predicate	Object
instanceOf	mathematical theorem ⓘ theorem in partial differential equations ⓘ
addresses	well-posedness of analytic Cauchy problems ⓘ
appearsIn	standard graduate textbooks on partial differential equations ⓘ
appliesTo	certain initial value problems for partial differential equations ⓘ certain nonlinear partial differential equations with analytic coefficients ⓘ linear partial differential equations with analytic coefficients ⓘ
assumes	PDE is solvable for the highest-order time derivative ⓘ
classification	local existence and uniqueness theorem ⓘ
concerns	local solutions near the initial hypersurface ⓘ
concernsOrder	finite-order partial differential equations ⓘ
domain	open subset of Euclidean space ⓘ
ensures	existence of a unique analytic solution in a neighborhood of the initial hypersurface ⓘ
field	mathematical analysis ⓘ partial differential equations ⓘ
guarantees	existence of local analytic solutions ⓘ uniqueness of local analytic solutions ⓘ
hasGeneralization	Cauchy–Kovalevskaya theorem on manifolds ⓘ linked to: Cauchy–Kovalevskaya theorem results for systems of analytic PDEs ⓘ
hasLimitation	gives only local results, not global existence ⓘ requires analyticity rather than mere smoothness ⓘ
hasVariant	Cauchy–Kovalevskaya–Kashiwara theorem ⓘ linked to: Cauchy–Kovalevskaya theorem
historicalPeriod	19th century ⓘ
influenced	development of modern PDE theory ⓘ theory of hyperbolic equations ⓘ
initialDataGivenOn	non-characteristic hypersurface ⓘ
isAnalogOf	Picard–Lindelöf theorem for ordinary differential equations ⓘ linked to: local existence and uniqueness theorem
isSpecialCaseOf	existence and uniqueness theorems for PDEs ⓘ
language	usually formulated over the real or complex numbers ⓘ
namedAfter	Augustin-Louis Cauchy ⓘ Sofya Kovalevskaya ⓘ linked to: Sofia Kovalevskaya
proofTechnique	majorant series method ⓘ power series expansion ⓘ
relatedTo	Cauchy problem ⓘ analytic continuation ⓘ non-characteristic surfaces ⓘ
requires	analytic coefficients ⓘ analytic initial data ⓘ non-characteristic condition for the initial hypersurface ⓘ
solutionType	complex-analytic solution ⓘ real-analytic solution ⓘ
usedIn	complex analysis in several variables ⓘ local existence theory for evolution equations ⓘ mathematical physics ⓘ theory of analytic PDEs ⓘ

How these facts were elicited