English

On Right Continuity in $(L^2)^3$ at All the Points of Energy-regularized Solutions for the 3D Navier-Stokes Equations

Analysis of PDEs 2024-07-15 v3

Abstract

In this note I provide the notion of energy-regularized solutions (ER-solutions) of the 3D Navier-Stokes equations. These solutions can be obtained via the standard Galerkin arguments. I prove that each ER-solution for the 3D Navier-Stokes system satisfies Leray-Hopf property. Moreover, each ER-solution is rightly continuous in the standard phase space HH endowed with the strong convergence topology.

Keywords

Cite

@article{arxiv.2301.05754,
  title  = {On Right Continuity in $(L^2)^3$ at All the Points of Energy-regularized Solutions for the 3D Navier-Stokes Equations},
  author = {Pavlo O. Kasyanov},
  journal= {arXiv preprint arXiv:2301.05754},
  year   = {2024}
}

Comments

Formula (2.6) is incorrect