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PreprintCC BY 4.0arXiv

Boundary-Driven Nonequilibrium for the Coulomb Landau Equation

  • Chanwoo Kim
  • Jinsol Seo
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Abstract

We establish a nonlinear theory of the Coulomb Landau equation in smooth bounded domains with non-isothermal diffuse reflection. We construct a stationary state, prove its perturbative uniqueness and global nonlinear stability, and establish exponential convergence when the wall temperature approaches its stationary profile exponentially. We also establish stationary and global nonlinear well-posedness for prescribed inflow, together with asymptotic stability. The analysis combines a critical kinetic integrability gain with finite-exponent velocity-gradient estimates near grazing, allowing the nonlinear Coulomb estimates to close without Lx∞ control of velocity gradients.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026boundarydriven,
  title = {{Boundary-Driven Nonequilibrium for the Coulomb Landau Equation}},
  author = {Chanwoo Kim and Jinsol Seo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30111},
  eprint = {2610.30111},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30111},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Boundary-Driven Nonequilibrium for the Coulomb Landau Equation
AU  - Chanwoo Kim
AU  - Jinsol Seo
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.30111
UR  - https://arxiv.org/abs/2610.30111
AB  - We establish a nonlinear theory of the Coulomb Landau equation in smooth bounded domains with non-isothermal diffuse reflection. We construct a stationary state, prove its perturbative uniqueness and global nonlinear stability, and establish exponential convergence when the wall temperature approaches its stationary profile exponentially. We also establish stationary and global nonlinear well-posedness for prescribed inflow, together with asymptotic stability. The analysis combines a critical kinetic integrability gain with finite-exponent velocity-gradient estimates near grazing, allowing the nonlinear Coulomb estimates to close without L_x^∞ control of velocity gradients.
ER  -