By the same derivation as we did for γ¯ we conclude that0<P0(u)<1−u,P0′(u)+1>0∀u∈(0,1). The key here is that P0 is a sub-solution and P1(u):=1−u is a super-solution of (2.5) with 0<κ<κ0 in the sense thatN[κ,P0]=(κ02−κ2)(P0+u)(1−u...
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Navier did use Lagrangean method for derivation of the law of Fluids 2019, 4, 5; doi:10.3390/fluids4010005 www.mdpi.com/journal/fluids Fluids 2019, 4, 5 2 of 20 motion; however, Stokes used—as we do it herein as well—the method introduced by Cauchy for separating material equation ...