English

Lorentz spaces in action on pressureless systems arising from models of collective behavior

Analysis of PDEs 2020-11-04 v2

Abstract

We are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in Lq,r(0,T;Lp(Ω))L_{q,r}(0,T;L_p(\Omega)) spaces.

Keywords

Cite

@article{arxiv.2005.05603,
  title  = {Lorentz spaces in action on pressureless systems arising from models of collective behavior},
  author = {Raphaël Danchin and Piotr Boguslaw Mucha and Patrick Tolksdorf},
  journal= {arXiv preprint arXiv:2005.05603},
  year   = {2020}
}