Uniqueness and nonuniqueness of the Stokes and Oseen flows

The uniqueness class for the solutions to the Cauchy problem for flows modeled by the time-dependent Stokes and Oseen systems of equations is determined as in the growth class C exp(α|x|2). An example of a type considered by Tychonoff [Mat. Sb. 42 (1935), 199–216] is given that establishes the lack of uniqueness for such Stokes and Oseen systems. Even for the incompressible Navier–Stokes system, an example shows that rapidly growing nonphysical mathematical solutions exist.