Global solutions for chemotaxis-Navier-Stokes system with Robin boundary conditions
Analysis of PDEs
2019-09-30 v1
Abstract
We consider a chemotaxis-Navier-Stokes system modelling cellular swimming in fluid drops where an exchange of oxygen between the drop and its environment is taken into account. This phenomenon results in an inhomogeneous Robin-type boundary condition. Moreover, the system is studied without the logistic growth of the bacteria population. We prove that in two dimensions, the system has a unique global classical solution, while the existence of a global weak solution is shown in three dimensions. In the latter case, we show that the energy is bounded uniformly in time. A key idea is to utilise a boundary energy to derive suitable {\it a priori} estimates. Moreover, we are able to remove the convexity assumption on the domain.
Keywords
Cite
@article{arxiv.1909.12547,
title = {Global solutions for chemotaxis-Navier-Stokes system with Robin boundary conditions},
author = {Marcel Braukhoff and Bao Quoc Tang},
journal= {arXiv preprint arXiv:1909.12547},
year = {2019}
}