Zygmund spaces, inviscid limits and uniqueness of Euler flows

Details Zygmund spaces, inviscid limits and uniqueness of Euler flows Zygmund spaces, inviscid limits and uniqueness of Euler flows

2007-03-29

arxiv.org/abs/math/0703881v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

10.1007/s00220-008-0452-2

The paper improves the classical uniqueness result for the Euler system in the $n$ dimensional case assuming that $\nabla u^E \in L_1(0,T;BMO(\Omega))$, only. Moreover the rate of the convergence for the inviscid limit of solutions to the Navier-Stokes equations is obtained, provided the same regularity of the limit Eulerian flow. A key element of the proof is a logarithmic inequality between the Hardy and $L_1$ spaces which is a consequence of the basic properties of the Zygmund space $\LlnL$.

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