  By calculating full symbol for the Dirichlet-to-Neumann map $\Lambda$ of a
Stokes flow, we establish the asymptotic expansion of the trace of the heat
kernel for $\Lambda$. We also give a useful procedure, by which all
coefficients of the asymptotic expansion can be explicitly calculated. These
coefficients are the Steklov spectral invariants of $\Lambda$, which provide
precise geometric information of the boundary for the Stokes flow. In
particular, the first two coefficients show that the area and (total) mean
curvature of the the boundary can be known by the Steklov eigenvalues of
$\Lambda$.
