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Using Landau Fermi liquid theory we derive a nonlinear non-adiabaticapproximation for the exchange-correlation (xc) vector potential defined by thexc stress tensor. The stress tensor is a local nonlinear functional of twobasic variables - the displacement vector and the second-rank tensor whichdescribes the evolution of momentum in a local frame moving with Eulerianvelocity. For irrotational motion and equilibrium initial state the dependenceon the tensor variable reduces to that on a metrics generated by a dynamicaldeformation of the system.Comment: RevTex, 5 pages, no figures. Final version published in PR

Local exchange-correlation vector potential with memory in time-dependent density functional theory: The generalized hydrodynamics approach