Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

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Equivalence of Invariant Measures and Stationary Statistical Solutions for The Autonomous Globally Modified Navier-Stokes Equations (2009, methodology): “In the next section, for technical reasons, we obtain a similar result on existence of solution (see Proposition 5 and Remark 6 below), using a different Galerkin approximation from that used in [3].”
Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier–Stokes equations (2019, methodology): “The above globally modified Navier-Stokes equations were initiated in the paper [3].”
Three dimensional system of globally modified Navier-Stokesequations with infinite delays (2010, background): “Then, taking into account (11), (12) and (19), reasoning as in [1] for the case without delays (see also [17] for the case of the Navier-Stokes system), we can pass to the limit in equation (13) and deduce that u is solution of d dt (u(t), v) + ν((u(t), v)) + 〈BN (u, u), v〉 = (f(t), v) + (ξg(t), v),”
The Uniqueness of Weak Solutions of the Globally Modified Navier-Stokes Equations (2009, methodology): “We prove uniqueness for the globally modified Navier-Stokes equations recently introduced by Caraballo, Real & Kloeden in [1] for initial conditions in the space H of square-summable divergence-free vector fields.”