Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#339828] of Siming He

Papers Published

  1. He, S; Tadmor, E, Suppressing Chemotactic Blow-Up Through a Fast Splitting Scenario on the Plane, Archive for Rational Mechanics and Analysis, vol. 232 no. 2 (May, 2019), pp. 951-986, Springer Nature America, Inc [doi]
    (last updated on 2020/07/12)

    © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. We revisit the question of global regularity for the Patlak–Keller–Segel (PKS) chemotaxis model. The classical 2D parabolic-elliptic model blows up for initial mass M> 8 π. We consider a more realistic scenario which takes into account the flow of the ambient environment induced by harmonic potentials, and thus retain the identical elliptic structure as in the original PKS. Surprisingly, we find that already the simplest case of linear stationary vector field, Ax ⊤ , with large enough amplitude A, prevents chemotactic blow-up. Specifically, the presence of such an ambient fluid transport creates what we call a ‘fast splitting scenario’, which competes with the focusing effect of aggregation so that ‘enough mass’ is pushed away from concentration along the x 1 -axis, thus avoiding a finite time blow-up, at least for M< 16 π. Thus, the enhanced ambient flow doubles the amount of allowable mass which evolve to global smooth solutions.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320