# Local well-posedness in the Wasserstein space for a chemotaxis model coupled to Navier-Stokes equations

## TL;DR

This paper proves the local well-posedness of a coupled chemotaxis and fluid dynamics model in the Wasserstein space, improving existence results by weakening initial data assumptions.

## Contribution

It refines the existence theory for a Keller-Segel-Navier-Stokes system by strengthening the analysis of the Fokker-Planck component in Wasserstein space.

## Key findings

- Existence of solutions under weaker initial data conditions
- Refined analysis of Fokker-Planck equation in Wasserstein space
- Construction of solutions with biological density in absolutely continuous curves

## Abstract

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. In the previous work [19], we established the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space using the optimal transportation technique. Exploiting this result, we constructed solutions of Keller-Segel-Navier-Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space. In this work, we refine the result on the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space. As a result, we construct solutions of Keller-Segel-Navier-Stokes equations under weaker assumptions on the initial data.