“…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…”
Section: Theorem 21 Let the Following Conditions Holdmentioning
In this note I provide the notion of energyregularized 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 H endowed with the strong convergence topology.
“…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…”
Section: Theorem 21 Let the Following Conditions Holdmentioning
In this note I provide the notion of energyregularized 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 H endowed with the strong convergence topology.
In this note we prove that each weak solution for the 3D Navier-Stokes system satisfies Leray-Hopf property. Moreover, each weak solution is rightly continuous in the standard phase space H endowed with the strong convergence topology.
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