Global existence and analyticity of Lp solutions to the compressible fluid model of Korteweg type

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'(& rho;*) = 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 & nu; over bar 2 > 4 & kappa; over bar , 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.& COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

This passage discusses a system of equations in Rd (d > 3) that describes the evolution of isothermal, viscous, and compressible fluids of Korteweg type, which can be used as a phase transition model. When the sound speed is zero, it is found that the linearized system has a purely parabolic structure, allowing for the establishment of global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of Lp-type. The proof mainly relies on new nonlinear Besov (-Gevrey) estimates for product and composition of functions. & COPY; 2023 Elsevier Inc. All rights reserved.