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Date | 2024-07-11 |
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Speaker | Sonae Hadama |

Dept. | Kyoto University |

Room | 27-116 |

Time | 16:00-18:00 |

In this talk, we consider the Hartree equation describing infinite quantum systems. It has infinitely many stationary solutions, and we are interested in their asymptotic stability. This problem is an analogy of the nonlinear Landau damping on the quantum side. In the known results, we need strong assumptions for both interactions and stationary solutions when $d \ge 4$. In this talk, we weaken the assumptions for both of them. There are two main difficulties: (1) How to get estimates with fractional derivatives, and (2) We cannot use Christ--Kiselev lemma. We will discuss these difficulties and how to overcome them. This talk is based on the joint work with Antoine Borie (University of Rennes) and Julien Sabin (University of Rennes).

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