分野別セミナー

There are many instances in nature where chemotaxis happens surrounded by a fluid. Several approaches considering this possibility have recently given rise to a significant number of mathematical models, coupling Keller-Segel type systems with Navier-Stokes equations. In an attempt to get some deeper insight into the role of current fluids during chemotactic aggregation, I will approach the case when the fluid flow is a given sink or else a source. When having a sink and radial symmetry in the initial data, I will show that after a previous deduction of a novel singular Moser-Trudinger type inequality, we get a new threshold condition for having global existence. Unlike the classical Keller-Segel model, this threshold condition depends not only on the total initial mass but also on the velocity of the fluid.