Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids

Boltzmann-Fermi-Dirac 方程的流体动力学极限：声学与 Stokes-Fourier

Hydrodynamic limits for the Boltzmann-Fermi-Dirac equation: Acoustic and Stokes-Fourier

本文在二维及以上环面上证明了 BFD 方程的声学和 Stokes-Fourier 流体动力学极限，通过改进弱解框架处理三次非线性，得到涨落的唯一极限。

Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.

Boltzmann方程组中气体混合物的声学极限

Acoustic limit of Boltzmann equations for gas mixture

本文研究了两种物种气体混合物Boltzmann方程组的水动力和声学极限，通过Hilbert展开法在小Knudsen数下构造了水动力极限，并严谨证明了声学极限，考虑了不同粒子质量带来的线性化碰撞算子的额外特性。

On asymptotic isotropy for a hydrodynamic model of liquid crystals

We study a PDE system describing the motion of liquid crystals by means of the $Q-$tensor description for the crystals coupled with the incompressible Navier-Stokes system. Using the method of Fourier splitting, we show that solutions of the system tend to the isotropic state at the rate $(1 + t)^{-3/2}$ as $t \to \infty$.

Homogenized models for a short-time filtration and for acoustic waves propagation in a porous media

We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic and a characteristic time of processes is small enough. Such kind of models may describe, for example, hydraulic fracturing or acoustic or seismic waves propagation. As the results, we derive different types of homogenized equations …

On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis

The hydrodynamic limit of a one dimensional kinetic model describing chemotaxis is investigated. The limit system is a conservation law coupled to an elliptic problem for which the macroscopic velocity is possibly discontinuous. Therefore, we need to work with measure-valued densities. After recalling a blow-up result in finite time of regular solutions for the hydrodynamic model, we establish a convergence result of the solutions of the kinetic model towards solutions of a problem limit defined thanks to the flux. Numerical simulations illustrate this convergence result.