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By calculating full symbol for the Dirichlet-to-Neumann map $\Lambda$ of aStokes flow, we establish the asymptotic expansion of the trace of the heatkernel for $\Lambda$. We also give a useful procedure, by which allcoefficients of the asymptotic expansion can be explicitly calculated. Thesecoefficients are the Steklov spectral invariants of $\Lambda$, which provideprecise geometric information of the boundary for the Stokes flow. Inparticular, the first two coefficients show that the area and (total) meancurvature of the the boundary can be known by the Steklov eigenvalues of$\Lambda$.

One can know the area and total curvatures of the boundary by hearing the resonances of a Stokes flow