Zygmund spaces, inviscid limits and uniqueness of Euler flows
Piotr B. Mucha, Walter M. Rusin
Abstract
The paper improves the classical uniqueness result for the Euler system in the n dimensional case assuming that ∇ uE ∈ L1(0,T;BMO(Ω)), 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 L1 spaces which is a consequence of the basic properties of the Zygmund space .
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