English

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 L1L^1 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 L3L^3, with finite first moment. Moreover, we describe the evolution starting from axisymmetric initial data. Our approach is purely Lagrangian.

Keywords

Cite

@article{arxiv.2303.05797,
  title  = {Lagrangian solutions to the transport--Stokes system},
  author = {Marco Inversi},
  journal= {arXiv preprint arXiv:2303.05797},
  year   = {2023}
}
R2 v1 2026-06-28T09:10:45.757Z