Small solids in an inviscid fluid

We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. Though this model can be considered simple, its mathematical analysis is tough. Several results are presented, according to the term of interaction (linear or quadratic) and we also describe numerical methods, which are analyzed and tested.