We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases with gamma between 1 and 2, including 1. The initial data of these solutions have constant densities and outward-swirling velocities. We use the axisymmetry and self-similarity assumptions to reduce the equations to a system of three ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. These solutions exhibit familiar structures seen in hurricanes and tornadoes. They all have finite local energy and vorticity with well-defined initial and boundary values.
Global smooth solutions of Euler equations for Van der Waals gases
本文证明了当$Hm$中密度足够小时，当$m$中密度足够大时，Van der Waals气体的Euler可压缩方程解的整体存在性.为此，我们引入了一个特定的对称性，允许零密度的区域。接下来，我们在$Hm$中进行估计，对某些项使用M所做的估计。Grassin，他在理想多方气体的更简单的情况下证明了同样的定理。由于其非线性，我们单独处理其余项。
Propagation of uniform boundedness of entropy and inhomogeneous regularities for viscous and heat conductive gases with far field vacuum in three dimensions
Shock formation for 3D steady supersonic flows with general short pulse data
School of Mathematical Sciences and IMS, Nanjing Normal University（南京师范大学数学科学学院及国际数学中心）；Institute of Mathematical Sciences, The Chinese University of Hong Kong（香港中文大学数学科学研究所）
Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients
本文研究了有界环形区域内可压缩导热理想多方气体的Navier-斯托克斯方程，其中粘性系数和导热系数是温度的一般光滑函数。一个全球的时间，球或圆柱对称，经典解的初始边值问题的存在唯一的和指数收敛到常数状态的时间趋于无穷的初始数据和绝热指数$γ$在一定的假设下。如果$γ$足够接近1，则初始数据可能很大。这些结果是Nishida-Smoller型的，并推广了[Liu et al.，SIAM J. Math. Anal. 46（2014），2185- 2228]限于一维流。
