Author:
Danchin Raphaël,Bogusław Mucha Piotr,Tolksdorf Patrick
Abstract
AbstractWe 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 $$L_{q,r}(0,T;L_p(\Omega ))$$
L
q
,
r
(
0
,
T
;
L
p
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Ω
)
)
spaces.
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
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