Abstract
We are concerned with a system of equations in Rd(d≥3) governing the evolution of isothermal, viscous and compressible fluids of Korteweg type, that can be used as a phase transition model. In the case of zero sound speed P′(ρ⁎)=0, it is found that the linearized system admits the purely parabolic structure, which enables us to establish the global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of Lp-type. Precisely, if the full viscosity coefficient and capillary coefficient satisfy ν¯2≥4κ¯, then the acoustic waves are not available in compressible fluids. Consequently, the prior L2 boundedness on the low frequencies of density and velocity could be improved to the general Lp version with 1≤p<d. The proof mainly relies on new nonlinear Besov (-Gevrey) estimates for product and composition of functions.
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