An elementary proof of existence and uniqueness for the Euler flow in uniformly localized Yudovich spaces

Speaker: Prof. Gianluca Crippa （University of Basel）

Title: An elementary proof of existence and uniqueness for the Euler flow in uniformly localized Yudovich spaces

Time&Venue: 2022.03.24 21:00-22:00 Zoom：924 888 5804  PW：AMSS2022

Abstract：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).