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arXiv · 1909.12547

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

Marcel Braukhoff·Bao Quoc Tang
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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.

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Marcel Braukhoff, Bao Quoc Tang. 2019-09-27. Global solutions for chemotaxis-Navier-Stokes system with Robin boundary conditions. https://arxiv.org/abs/1909.12547

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