LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN, PIOTR BOGUSLAW MUCHA AND PATRICK TOLKSDORF
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
$L_{q,r}(0,T;L_p(\Omega))$ spaces.
Domains
Analysis of PDEs [math.AP]
Origin : Files produced by the author(s)
Loading...