Phase and Test Function Spaces

Argument space, phase space, solution sets, and turbulence measure of the Navier-Stokes pdes are defined and their elementary properties presented for incompressible fluids and homogeneous boundary conditions. The argument/test function space is the domain of definition of the characteristic functional; it is considered for non-compact domains. Nuclear spaces are introduced for a solenoidal basis for the treatment of the characteristic functional and an example for a nuclear space is given.