Well-Posedness for a One-Dimensional Fluid-Particle Interaction Model
Boris Andreianov, Frédéric Lagoutière, Nicolas Seguin, Takéo Takahashi
Source abstract
The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503--3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singular Burgers equation is inspired by the theory of conservation laws with discontinuous flux developed by the first author, K. H. Karlsen, and N. H. Risebro in [Arch. Ration. Mech. Anal., 201 (2011), pp. 26--86]. In this paper, we prove well-posedness and justify an approximation strategy for the particle in Burgers system in the case of initial data of bounded variation. An existence result for data is also given.
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