Math @ Duke

Publications [#337289] of Siming He
Papers Published
 He, S, Suppression of blowup in parabolicparabolic PatlakKellerSegel via strictly monotone shear flows,
Nonlinearity, vol. 31 no. 8
(July, 2018),
pp. 36513688, IOP Publishing [doi]
(last updated on 2020/07/12)
Abstract: © 2018 IOP Publishing Ltd & London Mathematical Society Printed in the UK. In this paper we consider the parabolicparabolic PatlakKellerSegel models in T × ℝ with advection by a large strictly monotone shear flow. Without the shear flow, the model is L1 critical in two dimensions with critical mass 8π: solutions with mass less than 8π are global in time and there exist solutions with mass larger than 8π which blow up in finite time (Schweyer 2014 (arXiv:1403.4975)). We show that the additional shear flow, if it is chosen sufficiently large, suppresses one dimension of the dynamics and hence can suppress blowup. In contrast with the parabolicelliptic case (Bedrossian and He 2016 SIAM J. Math. Anal. 49 472266), the strong shear flow has destabilizing effect in addition to the enhanced dissipation effect, which makes the problem more difficult.


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