Counterexamples to \(L^p\) collapsing estimates

DOI10.1215/00192082-8886967zbMath1472.35354arXiv2002.08446OpenAlexW3165965266WikidataQ124883229 ScholiaQ124883229MaRDI QIDQ2039728

Xiumin Du, Matei Machedon

Publication date: 5 July 2021

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.08446

zbMATH Keywords

Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equationsHartree-Fock type equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55)

Cites Work

• On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
• Strichartz inequality for orthonormal functions
• Global well-posedness of the NLS system for infinitely many fermions
• Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics
• Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in \(d=3\) based on spacetime norms
• Pair excitations and the mean field approximation of interacting Bosons, II
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• Correlation Structures, Many-Body Scattering Processes, and the Derivation of the Gross–Pitaevskii Hierarchy
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
• Uniform in N estimates for a Bosonic system of Hartree–Fock–Bogoliubov type

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