On some modification Navier–Stokes equations Original Research Article

This article investigates some modification of the Navier–Stokes equations of type as the modification that was suggested by Lions (Quelques Methodes de Resolution des Problemes aux Limites Non Lineares, DUNOD, Gauthier-Villaris, Paris, 1969) in the form View the MathML source divu=0,(t,x)∈Q≡(0,T)×Ω,T>0,μ>0, View the MathML source under View the MathML source. In this we prove the existence theorem for the different pi⩾max{2,3−2/n} and, on some additional conditions (i.e. of the pi=p⩾4) in the isotropic nonlinearity case, we prove the uniqueness theorem for the considered problem.