In a recent paper , the global well-posedness of the two-dimensional Euler equation with vorticity in was proved, where LBMO is a Banach space which is strictly imbricated between and BMO. In the present paper we prove a global result on the inviscid limit of the Navier–Stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier–Stokes equations, independent of the viscosity, are also obtained.
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Frédéric Bernicot, Tarek Elgindi, Sahbi Keraani, On the inviscid limit of the 2D Navier–Stokes equations with vorticity belonging to BMO-type spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 597–619DOI 10.1016/J.ANIHPC.2014.12.001