the most common settings because the equation and its solutions are then consistent with special relativity. Another symmetry arises from gauge freedom, which is intrinsic to the field equations. Fields which correspond to interactions may be gauge fields, which means they can be derived from a potential, and certain values of potentials correspond to the same value of the field. Classification Field equations can be classified in many ways: classical or quantum, nonrelativistic or relativistic, according to the spin or mass of the field, and the number of components the field has and how they change under coordinate transformations (e.g. scalar fields, vector fields, tensor fields, spinor fields, twistor fields etc.). They can also inherit the classification of differential equations, as linear or nonlinear, the order of the highest derivative, or even as fractional differential equations. Gauge fields may be classified as in group theory, as abelian or nonabelian. Waves Field equations underlie wave equations, because periodically changing fields generate waves. Wave equations can be thought of as field equations, in the sense they can often be derived from field equations. Alternatively, given suitable Lagrangian or Hamiltonian densities and using the principle of stationary action, the wave equations can be obtained also. For example, Maxwell's equations can be used to derive inhomogeneous electromagnetic wave equations, and from the Einstein field equations one can derive equations for gravitational waves. Supplementary equations to field equations Not every partial differential equation (PDE) in physics is automatically called a "field equation", even if fields are involved. They are extra equations to provide additional constraints for a given physical system. "Continuity equations" and "diffusion equations" describe transport phenomena, even though they may involve fields which influence the transport processes. If a "constitutive equation" takes the form of a PDE and involves fields, it is not usually called a field equation because it does not govern the dynamical behaviour of the fields. They relate one field to another, in a given material. Constitutive equations are used along with field equations when the effects of matter need to be taken into account. Classical field equation Classical field equations arise in continuum mechanics (including elastodynamics and fluid mechanics), heat transfer, electromagnetism, and gravitation. Fundamental classical field equations include Newton's Law of Universal Gravitation for nonrelativistic gravitation. Einstein field equations for relativistic gravitation Maxwell's equations for electromagnetism. Important equations derived from fundamental laws include: Navier–Stokes equations for fluid flow.