About the existence of solutions in L2 spaces for a multidimensional incompressible flow under the k - epsilon turbulence model

Abstract

This study examines the multidimensional Navier–Stokes equations in conjunction with the k−ε turbulence model to establish the existence of weak solutions for the velocity vector, turbulent kinetic energy, and dissipation rate, denoted as (u,k,ε). Under certain conditions in external forces, initial, and boundary data, we prove that weak solutions exist within the L2 space. The provided result implies the existence and boundedness of solutions, which can be of help for further computational investigations under the scope of the k − ε turbulence model.