报告题目: Stability and instability of a generic non–conservative compressible two–fluid model
报告人：吴国春（华侨大学）
时间： 2023年2月22日, 9:30-10:30 (上午)
报告地点: 数学院425
邀请人：周建丰
报告摘要: We are concerned with stability and instability of the steady state $(1,0, 1, 0)$ for a generic non--conservative compressible two--fluid model in $R^3$. Under the assumption that the initial fraction densities are close to the constant state $(1,1)$ in $H^3\cap\dot B^{s}_{1,\infty}$ and the initial velocities are small in $H^2\cap \dot B^{s}_{1,\infty}$ with $s\in [0,1]$, it is shown that $\frac{1}{2}$ is the critical value of $s$ on the stability of the model in question. More precisely, when $0\leq s<\frac{1}{2}$, the steady state $(1,\overrightarrow{0},1,\overrightarrow{0})$
is nonlinearly globally stable; and conversely, the steady state $(1,\overrightarrow{0}, 1, \overrightarrow{0})$ is nonlinearly unstable in the sense of Hadamard when $\frac{1}{2}<s\le 1$.
报告人简介：吴国春，华侨大学副教授，硕士生导师，2014年在厦门大学获得理学博士学位.主要从事流体力学中的偏微分方程数学理论的研究，已在SIAM J. Math. Anal.、 J. Lond. Math. Soc.、 J. Funct. Anal.、J. Differential Equations.、Proc. Roy. Soc. Edinburgh Sect. A和Sci. China Math.等国内外权威期刊发表论文30多篇，主持国家自然科学基金青年项目1项和参与国家自然科学基金面上项目2项.
