Logarithmic Schrödinger equation and isothermal fluids

We consider the large time behavior in two types of equations, posed on whole space $\mathbb{R}^d$ : Schrödinger equation with a logarithmic nonlinearity one hand; compressible, isothermal, Euler, Korteweg and quantum Navier–Stokes equations other hand. explain some connections between families show how these may help having an insight all cases. insist specific aspects only, refer to cited articles for more details, complete statements. try give general picture results, present heuristical arguments that can intuition, which are not necessarily found mentioned articles.