Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

Jann-Long Chern; Maria Gualdani

Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

Analysis of PDEs 2022-07-19 v2

Authors: Jann-Long Chern , Maria Gualdani

Abstract

We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in the space $L^\infty(0,T,L^p(\R^3))$ for some $p>3/2$ . The proof uses a weighted Poincar\'e-Sobolev inequality recently introduced in \cite{GG18}.

Keywords

landau equation coulomb interactions weak solution uniqueness spatially homogeneous weighted poincaré-sobolev inequality higher integrable solution

Cite

@article{arxiv.1910.06216,
  title  = {Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions},
  author = {Jann-Long Chern and Maria Gualdani},
  journal= {arXiv preprint arXiv:1910.06216},
  year   = {2022}
}

Related papers

View all related →