报告题目：Well-posedness on MHD Equations with Partial or Fractional Dissipation
报 告 人：于幻
工作单位：北京信息科技大学
报告时间：2021-06-17 10:00-11:00
腾讯会议ID： 843 269 075
报告摘要：
In this talk, we consider the initial-value problem for the magnetohydrodynamic (MHD) equations with partial dissipation. We firstly prove the existence and uniqueness of solutions of the 2D MHD with only fractional magnetic diffusion $(-\Delta)^\beta b$ with any $\beta>1$ (without velocity dissipation) for the vorticity being in Yudovich-type space, by establishing some new time weighted estimates of the magnetic field, which indicates that the global regularity problem on the 2D MHD equations with only magnetic diffusion (without velocity dissipation) is critical. At last, the local exsitence and uniqueness of weak solutions with the minimal initial regularity assumption to the dD magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion are established.
In this talk, we consider the initial-value problem for the magnetohydrodynamic (MHD) equations with partial dissipation. We firstly prove the existence and uniqueness of solutions of the 2D MHD with only fractional magnetic diffusion $(-\Delta)^\beta b$ with any $\beta>1$ (without velocity dissipation) for the vorticity being in Yudovich-type space, by establishing some new time weighted estimates of the magnetic field, which indicates that the global regularity problem on the 2D MHD equations with only magnetic diffusion (without velocity dissipation) is critical. At last, the local exsitence and uniqueness of weak solutions with the minimal initial regularity assumption to the dD magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion are established.
In this talk, we consider the initial-value problem for the magnetohydrodynamic (MHD) equations with partial dissipation. We firstly prove the existence and uniqueness of solutions of the 2D MHD with only fractional magnetic diffusion $(-\Delta)^\beta b$ with any $\beta>1$ (without velocity dissipation) for the vorticity being in Yudovich-type space, by establishing some new time weighted estimates of the magnetic field, which indicates that the global regularity problem on the 2D MHD equations with only magnetic diffusion (without velocity dissipation) is critical. At last, the local exsitence and uniqueness of weak solutions with the minimal initial regularity assumption to the dD magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion are established.
报告人简介：
于幻，北京信息科技大学副教授。主要从事流体方程的数学理论研究，在ARMA, JFA, JDE, Nonlinearity等著名数学刊物上发表学术论文10余篇。曾访问普林斯顿大学，剑桥大学，香港中文大学。
