  In a well-known work, M. Anderson constructed a Hadamard manifold $(M^n, g)$
which carries non-zero $L^2$ harmonic $p$-forms when $p \neq n/2$, thus
disproving the Dodziuk-Singer conjecture. In this paper, we use the manifold
$(M^3, g)$ in order to solve another problem in geometric analysis, namely the
nonuniqueness of solutions of Leray-Hopf type of the Navier-Stokes equations.
