Laplace Equation

Important in fluid dynamics describing the behavior of gravitational and fluid potentials. The Laplace equation is fundamental in electromagnetism, astronomy, and fluid dynamics for describing electric, gravitational, and fluid potentials.

Laplace Equation

The Laplace equation is a second-order partial differential equation that describes the behavior of potentials in various fields:

Applications

  • Electromagnetism - Electric potentials
  • Astronomy - Gravitational potentials
  • Fluid Dynamics - Fluid potentials

General Form

In Cartesian coordinates, the Laplace equation is expressed as:

∇²φ = ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z² = 0

where φ represents the potential function.

Learn More

Wikipedia - Laplace's Equation

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Laplacian (∇²φ)-- potential units
Satisfies Laplace Equation--