Uniform Regularity and Vanishing Viscosity limit for the chemotaxis-Navier-Stokes system in a 3D bounded domain

TL;DR

This paper proves the existence of unique strong solutions for the 3D chemotaxis-Navier-Stokes system that are uniformly bounded regardless of viscosity, enabling the vanishing viscosity limit to the inviscid system.

Contribution

It establishes uniform regularity and the vanishing viscosity limit for the 3D chemotaxis-Navier-Stokes system in bounded domains, a novel result in this context.

Findings

Existence of unique strong solutions independent of viscosity

Uniform bounds in conormal Sobolev spaces

Successful passage to the inviscid limit

Abstract

We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis-Navier-Stokes system in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. It is shown that there exists a unique strong solution of the incompressible chemotaxis-Navier-Stokes system in a finite time interval which is independent of the viscosity coefficient. Moreover, the solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible inviscid chemotaxis-Navier-Stokes system.