The Stokes operator, named after George Gabriel Stokes, is an unbounded linear operator used in the theory of partial differential equations, specifically in the fields of fluid dynamics and electromagnetics.

Definition

as the Leray projection onto divergence free vector fields is defined by

is the Laplacian (usually n= are the standard Sobolev spaces is taken in the distribution sense.

Properties

is a self-adjoint positive-definite which satisfy

:

inner product.

is the trace operator is injective.

References

• Constantin, Peter and Foias, Ciprian. Navier-Stokes Equations, University of Chicago Press, (1988)