Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Well-posedness for the massive nonlinear wave equation on asymptotically AdS spacetimes

In this paper, we prove some well-posedness theorems for the nonlinear massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed by contraction mapping method and also as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

Z箍缩聚变及高能量密度应用研究进展

基于脉冲功率技术的Z箍缩过程可以实现驱动器电储能到X光辐射的高效率转换，形成极端温度、密度、压力条件，近年来在惯性约束聚变及高能量密度应用中取得了一系列重要进展。综述了国际上辐射间接驱动和磁直接驱动两条Z箍缩聚变技术路线发展现状，简要介绍了我国Z箍缩聚变尤其是7~8 MA脉冲功率装置上的动态黑腔研究进展；分别从辐射与物质相互作用、辐射不透明度、材料动态特性、实验室天体物理等方面，概述了Z箍缩应用于高能量密度物理研究的技术路线和主要成果。希望通过对Z箍缩聚变及高能量密度应用研究的论述和发展趋势分析，推动我国Z箍缩研究领域的进一步发展。     

On positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshes

Nonlinear Dynamics - The positivity preserving is one of the key requirements to discrete schemes for subdiffusion equation. The main goal of our research is to explore a spatial second-order...     

Applicability of ~9Be global optical potential to reactions of ~(7,10,11,12)Be

Elastic scattering angular distributions and total reaction cross-sections of ~(7,10,11,12)Be projectiles are predicted by the systematic ~9 Be global phenomenological optical model potential for target mass numbers ranging from24 to 209. These predictions provide a detailed analysis by their comparison with the available experimental data.Furthermore, these elastic scattering observables are also predicted for some targets out of the mass number range.The results are in reasonable agreement with the existing experimental data, and they are presented in this study.