Zygmund spaces, inviscid limits and uniqueness of Euler flows
arXiv:math/0703881 · doi:10.1007/s00220-008-0452-2
Abstract
The paper improves the classical uniqueness result for the Euler system in the dimensional case assuming that , 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 spaces which is a consequence of the basic properties of the Zygmund space $\LlnL$.
13 pages