Lagrangian solutions to the transport--Stokes system
Analysis of PDEs
2023-03-13 v1
Abstract
In this paper we consider the transport--Stokes system, which describes the sedimentation of particles in a viscous fluid in inertialess regime. We show existence of Lagrangian solutions to the Cauchy problem with initial data. We prove uniqueness of solutions as a corollary of a stability estimate with respect to the 1-Wasserstein distance for solutions with initial data in a Yudovich-type refinement of , with finite first moment. Moreover, we describe the evolution starting from axisymmetric initial data. Our approach is purely Lagrangian.
Cite
@article{arxiv.2303.05797,
title = {Lagrangian solutions to the transport--Stokes system},
author = {Marco Inversi},
journal= {arXiv preprint arXiv:2303.05797},
year = {2023}
}