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Sinks and sources in chemotactic aggregation

Hold Date
2017-10-31 12:00〜2017-10-31 13:00
Lecture Room S W1-C-504, West Zone 1, Ito campus, Kyushu University
Object person
Espejo, Eduardo (Faculty of Mathematics, Kyushu University)

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.