Optimal bounds for the inviscid limit of Navier–Stokes equations

Article type: Research Article

Authors: Abidi, H. | Danchin, R.^;

Affiliations: Laboratoire Jacques‐Louis Lions, Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France | Centre de Mathématiques, Université Paris 12, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France

Note: [] Corresponding author. E‐mail: [email protected].

Abstract: We consider the inviscid limit of incompressible two‐dimensional fluids with initial vorticity in L∞ and in some Besov space Bη2,∞ with low regularity index. We obtain a general result of strong convergence in L2 which applies to the case of vortex patches with smooth boundaries. The rate of convergence we find is (νt)3/4 (where ν stands for the viscosity and t, for the time). It improves the (νt)1/2 rate given by P. Constantin and J. Wu in (Nonlinearity 8 (1995), 735–742). Besides, it is shown to be optimal in the case of circular vortex patches.

Journal: Asymptotic Analysis, vol. 38, no. 1, pp. 35-46, 2004