Local null-controllability of the 2-D Vlasov-Navier-Stokes system
Analysis of PDEs
2016-07-20 v1
Abstract
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity field of the fluid from any initial state to the zero steady state, by means of an internal control. Indeed, we can modify the non-linear dynamics of the system in order to absorb the particles and let the fluid at rest. The proof is achieved thanks to the return method and a Leray-Schauder fixed-point argument.
Keywords
Cite
@article{arxiv.1607.05578,
title = {Local null-controllability of the 2-D Vlasov-Navier-Stokes system},
author = {Iván Moyano},
journal= {arXiv preprint arXiv:1607.05578},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1510.07210