洛仑兹空间对集体行为模型产生的无压系统的作用
Lorentz spaces in action on pressureless systems arising from models of collective behavior
摘要：
我们关注的是在天体物理学或集体行为中描述的无压气体模型的时间全局存在性和唯一性结果。初始数据是粗糙的：特别地，密度仅是有界的。我们的结果是基于插值和抛物极大正则性，其中洛伦兹空间起着关键作用。在$L_{q,r}(0,T;L_p(Ω))$空间中建立了抛物型方程组的一个新的极大正则性估计.
英文摘要：
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 $L_{q,r}(0,T;L_p(Ω))$ spaces.
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