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Scattering for the positive density Hartree equation

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arxiv 2504.19552 v1 pith:WK2WUHRQ submitted 2025-04-28 math.AP math-phmath.MP

Antoine Borie (IRMAR) , Sonae Hadama (RIMS) , Julien Sabin (IRMAR) This is my paper · ORCID
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keywords densityequationfractionalhartreematricespotentialsschattensobolev
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We study the asymptotic stability for large times of homogeneous stationary states for the nonlinear Hartree equation for density matrices in Rd for d\geq3. We can reach both the optimal Sobolev and Schatten exponents for the initial data, with a wide class of interaction potentials w (under the sole assumption that w is bounded, including in particular delta potentials). Our method relies on fractional Leibniz rules for density matrices to deal with the fractional critical Sobolev regularity s = d/2 -1 for odd d, as well as Christ-Kiselev lemmas in Schatten spaces.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering

    math.AP 2026-07 accept novelty 7.0 of 10

    Strong, quantitative convergence from Hartree to Vlasov is shown near Penrose-stable steady states, with uniform-in-time control of Wigner transforms and scattering profiles.

  2. Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle

    math.AP 2026-03 conditional novelty 7.0 of 10

    Subtracting the mean from the particle density improves orthonormal Strichartz estimates and shifts the optimal well-posedness threshold for the cubic NLS system on the circle from Schatten exponent 1 to 2.

  3. Large Time Behavior of the Klein-Gordon-Schr\"{o}dinger system

    math.AP 2025-06 conditional novelty 7.0 of 10

    Small localized data in H^4000 for the 3D Klein-Gordon-Schrödinger system produce global solutions that decay and scatter to free waves.

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