Classification of Partial Differential Equations

Refer to eqiation 1.1

if the equation is Parabolic

if the equation is Elliptic

if the equation is Hyperbolic

Unsteady Navier-Strokes equations are elliptic in space and parabolic in time.

At steady-state, the Navier-Stokes equations are elliptic.

In Elliptic problems, the boundary conditions must be applied on all confining surfaces. These are Boundary Value Problems.

A Physical Problem may be Steady or Unsteady.