Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

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

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.

反常颗粒气体的爆破分析

Blow up Analysis for Anomalous Granular Gases

在这篇文章中，我们调查的长时间行为的能量依赖的，空间均匀的，非弹性玻尔兹曼方程的硬球的解决方案。这个模型描述了一个稀释的气体组成的硬球的统计描述，在碰撞过程中耗散能量。我们假设气体是“反常的”，在这个意义上，能量耗散增加时，温度降低。这使得气体在有限的时间内冷却下来。我们研究了这个模型的爆破配置文件的存在性和唯一性，连同平衡的趋势和冷却法律相关联，推广经典的哈夫定律的颗粒气体。为此，我们通过引入新的强“非线性”自相似变量，研究了非弹性Boltzmann方程的渐近行为。

粘弹性颗粒气体的流体极限

The hydrodynamic limit of viscoelastic granular gases

本文首次严格推导了粘弹性颗粒气体的不可压缩Navier-Stokes-Fourier系统，并确定了颗粒温度的Haff定律。

变恢复系数颗粒气体的自由冷却和高能尾流

Free cooling and high-energy tails of granular gases with variable restitution coefficient

我们证明了所谓的广义哈夫定律产生的最佳代数冷却速率的颗粒气体的温度所描述的均匀玻尔兹曼方程的非弹性相互作用与非常数恢复系数。我们的分析是通过仔细研究的无限系统的时刻的解决方案的Boltzmann方程的颗粒气体和精确的Lp估计的自相似变量。在这个过程中，我们推广的玻尔兹曼碰撞算子最近获得的均匀颗粒气体与常数恢复系数的更广泛的一类物理恢复系数，取决于碰撞碰撞速度的几个结果。这个推广导致了所谓的L1指数尾定理。对于这个模型。

From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system

In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system of hydrodynamic equations describing granular flows and prove existence of classical solutions to the aforementioned system. One of the main issue is to identify the correct relation between the restitution coefficient (which quantifies the rate of energy loss at the microscopic level) and the Knudsen number which allows us to obtain non trivial hydrodynamic…

Trend to equilibrium for granular media equations under non-convex potential and application to log gases

We derive new HWI inequalities for the granular media equation, which external potential $V$ and interaction potential $W$ are only strictly convex on complementary parts of the space. Particularly, potentials are not assumed convex. After solving technicalities related to the singularity of a logarithmic $W$, we apply our result to obtain stability rates of log gases under non-strictly convex or quartic external potentials. We prove that the distribution of a log gas converges towards an equilibrium with respect to the Wasserstein distance at a square root rate. Finally, we establish exponent…