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The Landau equation: Well-posedness and singularities of homoenergetic solutions

  • Francisco-Unai Caja-Lopez
  • Maria Pia Gualdani
  • Alessia Nota
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Abstract

We consider the inhomogeneous Landau equation and focus on solutions whose density and temperature evolve in time but remain spatially homogeneous. Such solutions are called homoenergetic. We identify one class of initial data for which homoenergetic solutions exist globally in time, and another class for which they develop finite-time hydrodynamic singularities. The initial data are spatially inhomogeneous, neither close to vacuum nor close to equilibrium; both the well-posedness and the finite-time blow-up results hold for all soft and hard potentials.

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Cite

BibTeXRIS
BibTeX
@misc{cajalopez2026landau,
  title = {{The Landau equation: Well-posedness and singularities of homoenergetic solutions}},
  author = {Francisco-Unai Caja-Lopez and Maria Pia Gualdani and Alessia Nota},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05236},
  eprint = {2611.05236},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05236},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Landau equation: Well-posedness and singularities of homoenergetic solutions
AU  - Francisco-Unai Caja-Lopez
AU  - Maria Pia Gualdani
AU  - Alessia Nota
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05236
UR  - https://arxiv.org/abs/2611.05236
AB  - We consider the inhomogeneous Landau equation and focus on solutions whose density and temperature evolve in time but remain spatially homogeneous. Such solutions are called homoenergetic. We identify one class of initial data for which homoenergetic solutions exist globally in time, and another class for which they develop finite-time hydrodynamic singularities. The initial data are spatially inhomogeneous, neither close to vacuum nor close to equilibrium; both the well-posedness and the finite-time blow-up results hold for all soft and hard potentials.
ER  -