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

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TURW03 - Modelling and analysis of turbulent transport, mixing and scaling

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) Lp 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) Lp 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).

This talk is part of the Isaac Newton Institute Seminar Series series.

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