Lagrangian solutions to the transport--Stokes system

Marco Inversi

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arXiv · 2303.05797

Lagrangian solutions to the transport--Stokes system

Marco Inversi

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

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Marco Inversi. 2023-03-10. Lagrangian solutions to the transport--Stokes system. https://arxiv.org/abs/2303.05797

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