Non-uniqueness of solutions for 3D Navier-Stokes equations in bounded domains

2020/02/28 by Nguyen, Vu Thanh
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.12765

Abstract

This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are ∂_t u=νΔu- u⋅ ∇ u-∇ p+ f and div~u=0. The focus of this study is on the case where the boundary condition is defined as u⋅ n|_∂Ω=0. This paper demonstrates the existence of two distinct strong solutions to the Navier-Stokes equations under this boundary condition.

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