2019/12/21 by H. Beirão da Veiga, Jiaqi Yang, da Veiga, Hugo Beirão +1 · 1 citation
Computer Science · Engineering · Mathematics · #35Q30 #76A05 #76D03 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1912.10249
openalex publication_date 2019/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the classical Shinbrot's criteria to guarantee that a Leray-Hopf solution satisfies the energy equality follows trivially from the L4( (0 ,T)×Ω)) Lions-Prodi particular case. Moreover we extend Shinbrot's result to space coefficients r ∈ (3, 4) . In this last case our condition coincides with Shinbrot condition for r=4, but for r<4 it is more restrictive than the classical one, 2/p + 2/r = 1 . It looks significant that in correspondence to the extreme values r=3 and r=∞, and just for these two values, the conditions become respectively u ∈ L^∞(L3) and u ∈ L2(L^∞), which imply regularity by appealing to classical Ladyzhenskaya-Prodi-Serrin (L-P-S) type conditions. However, for values r∈ (3,∞) the L-P-S condition does not apply, even for the more demanding case 3