1、Zero shear viscosity limit and boundary layer for the Navier–Stokes equations of compressible fluids between two horizontal parallel plates
周文书（大连民族大学） Time: Sep 11 2:00-2:40pm
In this talk, we will focus on zero shear viscosity limit and boundary layer for the Navier–Stokes equations of compressible fluids between two horizontal parallel plates. We consider an initial-boundary problem for the three-dimensional Navier–Stokes equations of compressible fluids between two horizontal parallel plates, where heat conductivity κ may depend on both density ρ and temperature θ such that κ(ρ, θ) ≥ κ1 ≡ constant > 0, ∀ρ, θ > 0. We prove the global existence of strong solutions for large data and justify the zero shear viscosity limit as the shear viscosity μ goes to zero. Moreover, we establish the value μα with any α ∈ (0, 1/2) for the boundary layer thickness.
2、Expansion of a compressible non-barotropic fluid in vacuum
余荣锋（中山大学） Time: Sep 11 2:50-3:20pm
In this talk, we prove that a region occupied by viscous or inviscid compressible magnetohydrodynamic fluids surrounded by vacuum will expand at a linear rate in time, provided there are no singularities. Similarly, for the free boundary problem of the full compressible Navier-Stokes or Euler system, the diameter of the gas region will also grow linearly in time.
3、Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff
周玉龙（中山大学） Time: Sep 11 3:30-4:00pm
We give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non cutoff. The results disclose the link between the hyperbolic property resulting from the cutoff assumption and the smoothing property due to the long-range interaction. In particular, we give an affrmative answer to the question that there is no jump for the property that the collision operator with cutoff does not have spectrum gap but the operator without cutoff does have for the moderate soft potentials.
4、Global stability of large solutions to compressible Navier-Stokes equations in the whole space
黄景炽（中山大学） Time: Sep 11 4:10-4:40pm
In this talk, we will focus on the global-in-time stability for isentropic compressible Navier-Stokes equations in the whole space. Assuming that the density is bounded in some Holder space, we first obtain that the solution will converge to its equilibrium with an explicit rate which as the same as that for the heat equation. Based on this new decay estimates, we prove the general global-in-time stability of CNS for both 2D and 3D cases. Some related models are also considered. This is joint work with Lingbing He, Chao Wang and Yuhui Chen.
5、A Fixed Point Method for Nonlocal Total Variation Image Restoration
刘强（深圳大学） Time: Sep 11 4:50-5:20pm
Nonlocal total variation (NLTV) regularization was one of efficiently method used for the image restoration. It is able to both remove the noise and preserve repetitive textures and details of images. However, for the applications in practice, it is heavily limited due to its low computational speed, especially for the large scale problems. Many researchers have studied its fast computing method. In this report, we give a fixed method based on proximity algorithms to the nonlocal TV image restoration, which is proposed by Charles A. Micchelli, Lixin Shen, etc. . By this method,the origin variation model can be viewed as the composition of a convex function and a linear transformation. The numerical experiments show that the method can perform favorably and efficiently solve the nonlocal TV based image restoration problems.
6、A free boundary problem for planar compressible Hall-magnetohydrodynamic equations
陶强（深圳大学） Time: Sep 11 5:30-6:00pm
In this talk, we focus on the existence and uniqueness of the global classical solution for the planar compressible Hall-magnetohydrodynamic equations with large initial data. The system is supplemented with free boundary and smooth initial conditions. The proof relies on the bounds of the density and the skew-symmetric structure of the Hall term.