Mathematical Analysis Seminar

Academic Year 2022-2023

Invited Speaker: NGUYEN DINH THI (Department of Mathematics, Uppsala University, Sweden)

Title: Blow-up of 2D attractive Bose-Einstein condensates at the critical rotational speed.

Date & Time: 21, September, 2023, 10.00 a.m -12.00 a.m

Location: F207, University of Science, 227 Nguyen Van Cu street, District 5, Ho Chi Minh City, Vietnam

Abstract: We study the ground states of a 2D focusing non-linear Schrödinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value from below the system collapses to a profile obtained from the optimizer of a Gagliardo-Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching or even equal to the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular the blow-up profile remains independent of the rotation frequency.