报告题目: Global refined Fujita-Kato solution of 3-D inhomogeneous incompressible Navier-Stokes equations with large density

报告人：桂贵龙教授 (湘潭大学)

时间：  2024年11月17日, 9:00-10:00 (上午)

地点: 澳门新葡京娱乐城 203

邀请人：周建丰

报告摘要:  We investigate the global unique Fujita-Kato solution to the 3-D inhomogeneous incompressible Navier-Stokes equations (INS), with  initial velocity being sufficiently small in $\dot{B}^{\frac{1}{2}}_{2, \infty}$ and  with initial density  being bounded from above and below. We first prove the global existence of Fujita-Kato solution to the system (INS) if we assume in addition that the initial velocity $u_0\in \dot{H}^{\frac{1}{2}.$ While under the additional assumptions that the initial velocity $u_0\in  \dot{B}^{\frac{1}{2}}_{2,1}$  and initial density $\rho_0$ satisfying $\rho_0^{-1}-1\in \dot{B}^{\frac{1}{2}}_{6,1},$  we prove that all the norms of the solutions are uniformly controlled by the norm of the initial data.  This is a recent joint work with Profs. H. Abidi and P. Zhang.

报告人简介：桂贵龙，湘潭大学数学与计算科学学院教授，博士生导师。2010年毕业于中国科学院数学与系统科学研究院数学研究所，基础数学专业。2011年获第十届中国数学会钟家庆数学奖。主要研究流体力学方程组的数学理论，研究工作涉及非齐次不可压缩Navier-Stokes方程组及其相关模型的适定性与稳定性、流体力学方程组的自由边界问题、非线性薛定谔方程的半经典极限理论等, 论文发表在CPAM, CMP, ARMA, Adv. Math., CPDE, JMPA, JFA等国际数学杂志。