text: The convection–diffusion equation is a relatively simple equation describing flows, or alternatively, describing a stochastically-changing system. Therefore, the same or similar equation arises in many contexts unrelated to flows through space.
  *It is formally identical to the Fokker–Planck equation for the velocity of a particle.
  *It is closely related to the Black–Scholes equation and other equations in financial mathematics.
  *It is closely related to the Navier–Stokes equations, because the flow of momentum in a fluid is mathematically similar to the flow of mass or energy. The correspondence is clearest in the case of an incompressible Newtonian fluid, in which case the Navier–Stokes equation is: 
  where  is the momentum of the fluid (per unit volume) at each point (equal to the density  multiplied by the velocity ),  is viscosity,  is fluid pressure, and  is any other body force such as gravity. In this equation, the term on the left-hand side describes the change in momentum at a given point; the first term on the right describes the diffusion of momentum by viscosity; the second term on the right describes the advective flow of momentum; and the last two terms on the right describes the external and internal forces which can act as sources or sinks of momentum.