中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人： Prof. Gianluca Crippa（University of Basel）
题 目：An elementary proof of existence and uniqueness for the Euler flow in uniformly localized Yudovich spaces
时 间：2022.03.24（星期四）21:00-22:00
地 点：Zoom 会议号：924 888 5804 密码：AMSS2022
摘 要：I will revisit Yudovich’s well-posedness result for the 2-dimensional Euler equations. I will derive an explicit modulus of continuity for the velocity, depending on the growth in p of the (uniformly localized) L^p norms of the vorticity. If the growth is moderate at infinity, the modulus of continuity is Osgood and this allows to show uniqueness. I will also show how existence can be proved in (uniformly localized) L^p spaces for the vorticity. All the arguments are fully elementary, make no use of Sobolev spaces, Calderon-Zygmund theory, or Paley-Littlewood decompositions, and provide explicit expressions for all the objects involved. This is a joint work with Giorgio Stefani (SISSA Trieste).
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