Gevrey analyticity and decay for the compressible Navier-Stokes system with capillarity

We are concerned with an isothermal model of viscous and capillary compressible fluids derived by J. E. Dunn Serrin (1985), which can be used as a phase transition model. Compared the classical Navier-Stokes equations, there is smoothing effect on density that comes from terms. First, we prove global solutions critical regularity have been constructed in [11] second author B. Desjardins (2001), Gevrey analytic. Second, extend result to more general L p framework. As consequence, obtain algebraic time-decay estimates Besov spaces (and even exponential decay for high frequencies) any derivatives solution. Our approach partly inspired work Bae, Biswas \& Tadmor [2] dedicated incompressible requires our establishing new bilinear (of independent interest) involving product or composition functions. To best knowledge, this first pointing out analyticity fluids.