Inviscid limit of the inhomogeneous incompressible Navier–Stokes equations under the weak Kolmogorov hypothesis in $\mathbb{R}^3$

In this paper, we consider the inviscid limit of inhomogeneous incompressible Navier-Stokes equations under the weak Kolmogorov hypothesis in R. In particular, we first deduce the Kolmogorov-type hypothesis in R, which yields the uniform bounds of α-order fractional derivatives of √ ρμu in Lx for some α > 0, independent of the viscosity. The uniform bounds can provide strong convergence of √ ρμu in L space. This shows that the inviscid limit is a weak solution to the corresponding Euler equations.