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We study the slow dynamics of metastable liquids using models obtained from analysing the equations of fluctuating nonlinear hydrodynamics (FNH). Constructions of these models in respective cases of one and two component systems involve taking into consideration the effects of  non-local and nonlinearcoupling of slowly decaying hydrodynamic fluctuations. For a one component simple liquid, we study integral equations for two and multi particle correlation functions of collective density fluctuations \cite{nb1,nb2,nb3}.  We also study the relaxation of single particle modes and self-diffusion process.  Here we apply the adiabatic-approximation, which assumes that for the glassy state, decay of momentum fluctuations occur much faster compared to that of number density.  From the two point correlation functions, renormalized due to the nonlinear dynamics described by FNH equations, we obtain the generalized viscosities and asymptotic relaxation times.  Calculations of self-diffusion coefficients and relaxation times allow us to test the validity of Stokes-Einstein relation in the metastable state.   Single particle and collective correlations in the dense liquid relaxes in different manners.  In recent years  this  has been observed in experiments with soft colloids .
In the same analysis we also calculate  multi particle correlations and identify dynamic correlation length. The latter is often referred to as dynamical heterogeneities of a glassy state. The present approach links findings of several previous computer simulation studies as well as schematic models. Here only the structure of the liquid  or the interaction potential between the particles  is used as in put in the model calculation.  From the study of  single particle dynamics in terms of correlation functions, we also estimate the fraction of particles which remain self-pinned for long times. The present approach with FNH equations are also extended to the case of binary mixtures. The diffusion constants$D_S$ for a tagged particle of species $s$, ($=1,2$)  of a binary mixture  depend on themass ratio $\kappa=m_2/m_1$ of the two constituents. The MCT shows that for nearlyequal sized particles, the two self diffusion coefficients  are related as $D_1{\sim}D_2^a$ with a non universalexponent $a$ and this relation holds over a wide range of $\kappa$values.