Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces

We are concerned with a system of equations governing the evolution isothermal, viscous, and compressible fluids Korteweg type, which is used to describe two-phase liquid–vapor mixture. It found that there “regularity-gain" dissipative structure linearized systems in case zero sound speed P′(ρ*)=0, comparison classical Navier–Stokes equations. First, we establish global-in-time existence strong solutions hybrid Besov spaces by using Banach’s fixed point theorem. Furthermore, prove global critical regularity Gevrey analytic fact. Secondly, based on Gevrey’s estimates, obtain uniform bounds growth analyticity radius negative spaces, lead optimal time-decay estimates their derivatives arbitrary order.