Global Well-posedness of the Chemotaxis-Navier-Stokes Equations in two dimensions

2015/03/24 by Chae, Myeongju, Kang, Kyungkeun, Lee, Jihoon +1
#35Q30 #35Q35 #76Bxx #76Dxx #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.06901

Abstract

We consider two dimensional Keller-Segel equations coupled with the Navier-Stokes equations modelled by Tuval et al.[32]. Assuming that the chemotactic sensitivity and oxygen consumption rate are nondecreasing and differentiable, we prove that there is no blow-up in a finite time for solutions with large initial data to chemotaxis-Navier-Stokes equations in two dimensions. In addition, temporal decays of solutions are shown, as time tends to infinity.

Related

• Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations
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• Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Poiseuille flow
• Exploring numerical blow-up phenomena for the Keller-Segel-Navier-Stokes equations