Functional-analytic methods for partial differential equations, Proc. Conf. Symp., Tokyo/Jap. 1989, Lect. Notes Math. 1450, 53-63 (1990).
[For the entire collection see Zbl 0707.00017.]
It is well known, that the Cauchy problem for the Navier-Stokes equations
has a global strong solution, provided is small, see the author [Math. Z. 187, 471-480 (1984; Zbl 0537.35065)]. The author shows, that one can obtain more information, namely the existence of several types of Lyapunov functions. Special types are the norms (for , if , which decrease monotonically in time provided is small enough.