Construction of High Regularity Invariant Measures for the 2D and 3D Euler Equations and Remarks on the Growth of the Solutions

25 Feb 2020 Latocca Mickaël

We consider the Euler equations on the torus in dimensions $2$ and $3$ and we construct invariant measures for the dynamics of these equations concentrated on sufficiently regular Sobolev spaces so that strong solutions are also known to exist at least locally. The proof follows the method of Kuksin, and we obtain in particular that these measures do not have atoms, excluding trivial invariant measures such as diracs... (read more)

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