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.

中文翻译：

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集体行为模型在无压系统上起作用的洛伦兹空间

我们关注无压力气体模型的全局及时性存在和唯一性结果，这些模型出现在天体物理学或集体行为现象的描述中。初始数据很粗糙：特别是密度是有界的。我们的结果基于插值和抛物线最大正则性，其中Lorentz空间起着关键作用。我们为\（L_ {q，r}（0，T; L_p（\ Omega））\）空间中的抛物线系统建立了一个新颖的最大正则估计。