The energy conservation and regularity for the Navier-Stokes equations

2021/07/09 by Tan, W., Yin, Z.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.04157

Abstract

In this paper, we consider the energy conservation and regularity of the weak solution u to the Navier-Stokes equations in the endpoint case. We first construct a divergence-free field u(t,x) which satisfies lim_{t→ T}√(T-t)||u(t)||_BMO0. Furthermore, we prove that if ||u₃||_{L^2,∞([0,T];BMO(ℝ³))}=M

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