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Abstract We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty [14] and Bresch-Jabin-Wang [8], which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of [8, 14], as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proven.
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Local Decay Estimates
Abstract We give a proof of local decay estimates for Schrödinger-type equations, which is based on the knowledge of Asymptotic Completeness. This approach extends to time dependent potential perturbations, as it does not rely on Resolvent Estimates or related methods. Global in time Strichartz estimates follow for quasi-periodic time-dependent potentials from our results.
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- Award ID(s):
- 2205931
- PAR ID:
- 10635594
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Archive for Rational Mechanics and Analysis
- Volume:
- 249
- Issue:
- 2
- ISSN:
- 0003-9527
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/s00205-025-02089-w
