应兰州大学数学与统计学院徐浩副教授邀请，华东理工大学曹玥副教授与安徽理工大学张昭云博士将于2026年4月12日下午做线上学术报告，期待各位老师与同学参加。

报告题目(I)：On regular solutions for two dimensional non-isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum

报告时间：2026年4月12日14:00—15：00

腾讯会议ID：583-478-723

报告摘要：We consider the Cauchy problem for the two dimensional (2D) non-isentropic compressible Navier-Stokes equations with zero thermal conductivity. For the temperature-dependent viscosity coefficients, we establish the local existence and uniqueness of regular solutions with arbitrary large initial data and far field vacuum in some inhomogeneous Sobolev spaces. Several challenges are encountered in this study: the appearance of vacuum causes degeneracies in both the time evolution and the spatial dissipation operators, the failure of the critical Sobolev embedding, and the absence of thermal conduction effects leads to the smooth effect missing. To prove the existence, we first develop an intrinsic singular structure of the nonlinear system by introducing some new variables, which actually helps us to overcome the degeneracy difficulties. Then, based on careful analysis of its intrinsic structure and the characteristics of special Sobolev embedding in $\mathbb{R}^2$, we successfully derive some new singular weighted energy estimates for regular solutions and finally establish the well-posedness via the classical iterative method.

报告人简介

曹玥，华东理工大学数学学院副教授。主要研究非线性偏微分方程组，关注可压缩Navier-Stokes方程组光滑解的整体/局部适定性理论和解的长时间行为，特别是输运系数依赖密度或温度的物理情形。研究论文发表在CVPDE、SIAM等学术期刊上，主持青年基金一项。

报告题目(II)：Global weak solution of compressible Vlasov-Navier-Stokes equations

报告时间：2026年4月12日15:00—16：00

腾讯会议ID：583-478-723

报告摘要：This work establishes the existence of weak solution to the Vlasov equation coupled with the barotropic compressible Navier-Stokes equation. The fluid velocity field is assumed to satisfy the no-slip boundary condition. Moreover, we assume that the kinetic distribution function satisfies either the nonhomogeneous Dirichlet boundary condition or the specular reflection boundary condition, for which the proofs rely respectively on the viscosity vanishing limit theory and the compactness argument.

报告人简介

张昭云，2022年博士毕业于中山大学，2022-2024在上海交通大学做博士后。现为安徽理工大学数学与大数据学院，中科大-安理工数学基础科学中心讲师。主要研究领域为不可压流体方程组的适定性和渐进行为等理论。曾获博士后面上项目。

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年4月9日