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Dichotomy index for well-posedness and ill-posedness
报告人:Weiliang Xiao (Nanjing Unversity of Finance & Economics) 时间:2021年11月12日10:30-11:30 字号:



Abstract: The attempt to search the largest functional spaces in which the well-posedness holds for Navier-Stokes equation led to a dichotomy phenomenon. The well-posedness method developed by Fujita and Kato, together with the ill-posedness method developed by Bourgain, Pavlović, Bejenaru, Tao et. al. make it become a reality that the dichotomy index existence. In this talk, I will track the well-posedness and ill-posedness results for Navier-Stokes equation, especially the results in the largest Besov space. The method developed in this issue also spreads to various fluid systems. This allow us to seek the dichotomy index in Besov spaces or Fourier-Besov spaces in Keller-Segel system, which the well-posedness holds if less than the index while the ill-posedness holds when bigger than it.

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