Euler equations

E32276

conservation law fluid dynamics equation system of partial differential equations

The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (5)

Label	Occurrences
Euler equations canonical	2
Euler equation	1
Euler equations (hydrodynamic limit)	1
Euler equations of fluid motion	1
Kelvin circulation theorem	1

Statements (51)

Predicate	Object
instanceOf	conservation law ⓘ fluid dynamics equation ⓘ system of partial differential equations ⓘ
appliesTo	compressible flow ⓘ incompressible flow ⓘ inviscid flow ⓘ
assumes	continuum hypothesis ⓘ inviscid fluid ⓘ zero viscosity ⓘ
describes	motion of an ideal fluid ⓘ
dimension	one-dimensional form ⓘ three-dimensional form ⓘ two-dimensional form ⓘ
expresses	conservation of energy ⓘ conservation of mass ⓘ conservation of momentum ⓘ
field	applied mathematics ⓘ continuum mechanics ⓘ fluid dynamics ⓘ
hasComponent	continuity equation ⓘ energy equation ⓘ momentum equation ⓘ
hasFormulation	conservative form ⓘ nonconservative form ⓘ primitive variable form ⓘ vector form ⓘ
hasProperty	Galilean invariant ⓘ can develop discontinuities ⓘ can develop shock waves ⓘ time-dependent ⓘ
hasUnknown	density field ⓘ fluid velocity field ⓘ internal energy or temperature field ⓘ pressure field ⓘ
isLimitCaseOf	Navier–Stokes equations ⓘ surface form: Navier–Stokes equations with zero viscosity
mathematicalType	hyperbolic system ⓘ nonlinear partial differential equation ⓘ
namedAfter	Leonhard Euler ⓘ
relatedTo	Bernoulli equation ⓘ Navier–Stokes equations ⓘ potential flow theory ⓘ
requires	equation of state ⓘ
solvedBy	Godunov-type schemes ⓘ finite difference methods ⓘ finite volume methods ⓘ spectral methods ⓘ
usedIn	aerodynamics ⓘ astrophysical fluid dynamics ⓘ compressible aerodynamics ⓘ gas dynamics ⓘ weather and climate modeling ⓘ

How these facts were elicited

The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.

Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
- If you don't know the subject at all, return an empty list.
- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: Euler equations
Description of subject: The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.

Referenced by (6)

Full triples — surface form annotated when it differs from this entity's canonical label.

Navier–Stokes equations → relatedTo → Euler equations ⓘ

New Keynesian economics → usesTool → Euler equations ⓘ

Boltzmann equation → hasLimit → Euler equations ⓘ

this entity surface form: Euler equations (hydrodynamic limit)

Bjerknes circulation theorem (applications in meteorology) → relatedTo → Euler equations ⓘ

subject surface form: Bjerknes circulation theorem

this entity surface form: Kelvin circulation theorem

Bernoulli equation → relatedConcept → Euler equations ⓘ

this entity surface form: Euler equations of fluid motion

Jeans instability → governingEquations → Euler equations ⓘ

this entity surface form: Euler equation