Anomalous Dissipation for the d-dimensional Navier-Stokes Equations

2023/07/13 by Jinlu Li, Li, Jinlu, Yanghai Yu +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies

paper · pdf · doi:10.48550/arxiv.2307.06812

Abstract

The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begincases ∂_tu^ε+u^ε⋅ ∇ u^ε-εΔu^ε+∇ p^ε=0,
div u^ε=0. \endcases We aim to presenting a simple rigorous examples of initial data which generates the corresponding solutions of the Navier--Stokes equations do exhibit anomalous dissipation. Precisely speaking, we show that there are (classical) solutions for which the dissipation rate of the kinetic energy is bounded away from zero.

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