Global solutions for chemotaxis-Navier-Stokes system with Robin boundary conditions

[摘要] 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 one or 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 introduce and utilise a boundary energy to derive suitable a priori estimates. Moreover, we are able to remove the convexity assumption on the domain. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-05

[关键词] Chemotaxis-Navier-Stokes systems;Robin boundary conditions;Global existence;Weak (classical) solutions;Boundary energy