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• W2894101260 abstract "We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for compressible fluids in $mathbb{R}^3$. Motivated by the Kolmogorov hypothesis (1941) for incompressible flow, we introduce a Kolmogorov-type hypothesis for barotropic flows, in which the density and the sonic speed normally vary significantly. We then observe that the compressible Kolmogorov-type hypothesis implies the uniform boundedness of some fractional derivatives of the weighted velocity and sonic speed in the space variables in $L^2$, which is independent of the viscosity coefficient $mu>0$. It is shown that this key observation yields the equicontinuity in both space and time of the density in $L^gamma$ and the momentum in $L^2$, as well as the uniform bound of the density in $L^{q_1}$ and the velocity in $L^{q_2}$ independent of $mu>0$, for some fixed $q_1 >gamma$ and $q_2 >2$, where $gamma>1$ is the adiabatic exponent. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations for barotropic fluids in $mathbb{R}^3$. Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of $mu>0$, that is in the high Reynolds number limit." @default.
• W2894101260 created "2018-10-05" @default.
• W2894101260 creator A5018452636 @default.
• W2894101260 creator A5038334215 @default.
• W2894101260 date "2019-12-01" @default.
• W2894101260 modified "2023-10-17" @default.
• W2894101260 title "Kolmogorov-type theory of compressible turbulence and inviscid limit of the Navier–Stokes equations in R3" @default.
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• W2894101260 doi "https://doi.org/10.1016/j.physd.2019.06.004" @default.
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