Existence of Solutions for time-dependent fractional Kohn-Sham Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916071969128448 |
|---|---|
| author | Breteaux, Sébastien Fantechi, Michele Faupin, Jérémy |
| author_facet | Breteaux, Sébastien Fantechi, Michele Faupin, Jérémy |
| contents | We consider time-dependent Kohn-Sham equations in dimension $3$ with a fractional dispersion relation $(1-Δ)^s$, $s\in(0,\frac32)$, and a class of interaction terms including, in particular, external potentials, internal potentials associated to Hartree-type non-linearities, and exchange terms described by energy subcritical pure-power non-linearities. We prove the local existence of weak solutions in $H^s$ using an approximation procedure regularizing the non-linearities. Assuming that the interaction energies can be controlled by the kinetic energy, we show that the solutions can be extended to global solutions using energy estimates. If $s\in[1,\frac32)$, we establish in addition the well-posedness of the time-dependent Kohn-Sham equations using Strichartz estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01321 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of Solutions for time-dependent fractional Kohn-Sham Equations Breteaux, Sébastien Fantechi, Michele Faupin, Jérémy Analysis of PDEs Mathematical Physics We consider time-dependent Kohn-Sham equations in dimension $3$ with a fractional dispersion relation $(1-Δ)^s$, $s\in(0,\frac32)$, and a class of interaction terms including, in particular, external potentials, internal potentials associated to Hartree-type non-linearities, and exchange terms described by energy subcritical pure-power non-linearities. We prove the local existence of weak solutions in $H^s$ using an approximation procedure regularizing the non-linearities. Assuming that the interaction energies can be controlled by the kinetic energy, we show that the solutions can be extended to global solutions using energy estimates. If $s\in[1,\frac32)$, we establish in addition the well-posedness of the time-dependent Kohn-Sham equations using Strichartz estimates. |
| title | Existence of Solutions for time-dependent fractional Kohn-Sham Equations |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2606.01321 |