Friday, July 14, 2023 - 12:00 in ZiF
Recent progress on multi-bubble blow-ups and multi-solitons to focusing (stochastic) non-linear Schrödinger equations
A talk in the SPDEs, optimal control and mean field games series by
Deng Zhang from Shanghai
| Abstract: |
We mainly review the recent results on multi-bubble blow-ups and multi-solitons
to the focusing (stochastic) nonlinear Schrödinger equations. In the mass-critical
case, the construction and conditional uniqueness of multi-bubble Bourgain-Wang
type blow-up solutions will be presented, which provide new examples for the
mass quantization conjecture. In the deterministic case without noise, this
also gives first examples of non-pure multi-solitons (including dispersive part)
for the soliton resolution conjecture. Further refined uniqueness of pure multi-bubble
blow-ups and multi-solitons in the very low asymptotic regime is obtained. At
last, in both the mass critical and subcritical cases, we also show the direct
construction of stochastic multi-solitons, particularly, in the absence of the
classical pseudo-conformal symmetry.
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