WELL-POSEDNESS FOR A ONE-DIMENSIONAL FLUID-PARTICLE INTERACTION MODEL
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | WELL-POSEDNESS FOR A ONE-DIMENSIONAL FLUID-PARTICLE INTERACTION MODEL |
| Type de publication | Journal Article |
| Year of Publication | 2014 |
| Auteurs | Andreianov B, Lagoutiere F, Seguin N, Takahashi T |
| Journal | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
| Volume | 46 |
| Pagination | 1030-1052 |
| Type of Article | Article |
| ISSN | 0036-1410 |
| Mots-clés | Burgers equation, BV estimates, fixed point, fluid-particle interaction, nonconservative coupling, splitting, Wave-front tracking, well-posedness |
| Résumé | 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 L infinity data is also given. |
| DOI | 10.1137/130907963 |