  In the paper, we establish commutator estimates for the Dirichlet-to-Neumann
map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's
bilinear estimates, and the results may be regarded as an extension of
[Dahlberg, Poisson semigroups and singular integrals, Proc. Amer. Math. Soc.,
97(1986), no.1, 41-48.] and [Shen, Commutator estimates for the
Dirichlet-to-Neumann map in Lipschitz domains, Some topics in harmonic analysis
and applications, 369C384, Adv. Lect. Math. (ALM)34, Int. Press, Somerville,
MA, 2016.] to Stokes systems.
