An elementary proof of existence and uniqueness for the Euler flow in uniformly localized Yudovich spaces
Duration: 39 mins 24 secs
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About this item
| Description: |
Gianluca Crippa (Universität Basel)
10 March 2022 – 11:15 to 12:15 |
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| Created: | 2022-03-11 09:52 |
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| Collection: | Mathematical aspects of turbulence: where do we stand? |
| Publisher: | Isaac Newton Institute |
| Copyright: | Gianluca Crippa |
| Language: | eng (English) |
| 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). |
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