Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations

Abstract

In this paper we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.

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

“…where z := Π s,T z ∈ C([s, T ]; H w ) ∩ L 2 (s, T ; V ), and dz dt is the derivative of z in the sense of distributions D * ((s, T ); V * ). When s = τ such problem was considered in [17,11,12,14,15,18,26] and references…”

Leray-Hopf and Continuity Properties for All Weak Solutions for the 3D~Navier-Stokes Equations

“…in the sense of distributions; cf. Kapustyan et al [9,10]; Kasyanov et al [11,12]; Melnik and Toscano [14]; Zgurovsky et al [19,Chapter 6].…”