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The present paper deals with the Cauchy problem of a multi-dimensionalnon-conservative viscous compressible two-fluid system. We first study thewell-posedness of the model in spaces with critical regularity indices withrespect to the scaling of the associated equations. In the functional settingas close as possible to the physical energy spaces, we prove the unique globalsolvability of strong solutions close to a stable equilibrium state.Furthermore, under a mild additional decay assumption involving only the lowfrequencies of the data, we establish the time decay rates for the constructedglobal solutions. The proof relies on an application of Fourier analysis to acomplicated parabolic-hyperbolic system, and on a refined time-weightedinequality.

On the well-posedness and decay rates of strong solutions to a multi-dimensional non-conservative viscous compressible two-fluid system