For the incompressible Euler flows in planar bounded domains $\Omega$, we prove that the vortex concentrating at the harmonic center of  $\Omega$ causes the existence of vortexes with small vorticities near the boundary. These results are very different from the known results for the multivortex flows in which all the local vorticities are of the same orders.  

　　Publication:  

　　SIAM Journal on Mathematical Analysis, Volume 55, Issue 5 , 2023  

　　http://dx.doi.org/10.1137/22M1500186  

　　Author:  

　　Daomin Cao  

　　Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China and University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China.  

　　Email: dmcao@amt.ac.cn  

　　Shusen Yan  

　　School of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China.  

　　Weilin Yu  

　　Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, People’s Republic of China  

　　Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China.