  The floating structure problem describes the interaction between surface
water waves and a floating body, generally a boat or a wave energy converter.
As shown by Lannes in [18] the equations for the fluid motion can be reduced to
a set of two evolution equations on the surface elevation and the horizontal
discharge. The presence of the object is accounted for by a constraint on the
discharge under the object; the pressure exerted by the fluid on this object is
then the Lagrange multiplier associated to this constraint. Our goal in this
paper is to prove the well-posedness of this fluid-structure interaction
problem in the shallow water approximation under the assumption that the flow
is axisymmetric without swirl. We write the fluid equations as a quasilinear
hyperbolic mixed initial boundary value problem and the solid equation as a
second order ODE coupled to the fluid equations. Finally we prove the local in
time well-posedness for this coupled problem, provided some compatibility
conditions on the initial data are satisfied.
