In this work we address various properties of electron gas in a strongly inhomogeneous situation. We consider s Luttinger model in external field which results provide us with the motivation for formulating our hydrodynamic model. This model results in a very simple profile equation which we apply to the problem of heavy impurity in a electron gas. Numerical results are presented for 2D case, and discussed for 3D. Later we apply the model to arrive at some experimentally tractable properties of electron liquid in both 2D and 3D, such as the effective electron mass at the Fermi surface, as well as the stopping power of electron gas with respect to the heavy repulsive intruders.; In this work we have tried to bring together an immense amount of the literature (and data) on the question of the fundamental excitations in electron liquids.
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