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发表时间:2021-01-12 阅读次数:696次
报告题目: On 3D Hall-MHD equations with fractional Laplacians: global well-posedness
报 告 人:张华丽
报告人所在单位:长沙理工大学
报告日期:2021-01-12 星期二
报告时间:10:30
报告地点:HGD2001
  
报告摘要:
In this talk, we will study the Cauchy problem for 3D incompressible Hall-MHD equations with fractional Laplacians $(-\Delta)^{\frac{1}{2}}$. The well-posedness of 3D incompressible Hall-MHD equations remains an open problem with fractional diffusion $(-\Delta)^{\beta}, \beta\in (0, {\frac{1}{2}}]$. In our talk, we first present the global well-posedness of small-energy solutions with general initial data in $H^s$, $s>\frac{5}{2}$. Second, a special class of large-energy initial data is constructed, with which the Cauchy problem is globally well-posed. The proofs rely upon a new global bound of energy estimates involving Littlewood-Paley decomposition and Sobolev inequalities, which enables one to overcome the $\frac{1}{2}$-order derivative loss of the magnetic field. This is a joint work with Kun Zhao.
  
本年度学院报告总序号:6

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