Floating structures in shallow water: local well-posedness in the axisymmetric case

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

Financial Markets imperfections, heterogeneity and growth

This paper offers a model of growth with heterogeneous agents in which, due to asymmetric information, financial markets do not work properly. In such a world, the Modigliani-Miller theorem fails to hold, a financial hierarchy emerges and ‘how to finance’ the engine of growth – in our case represented by uncertain endeavours in R&D - matters. In turn, heterogeneity means that agents lack sufficient information on the behaviour adopted by the others, forcing them to make use of naive rules in forming expectations and in calculating their probability of bankruptcy. The basic properties of the model are explored via simulations. In particular, it is possible to appreciate how a worsening of financial conditions (e.g. an increase of the contractual interest rate on loans or of the probability of bankruptcy) affects negatively the long-run average rate of growth