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

Zihao Song and Jiang Xu ()
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Zihao Song: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China
Jiang Xu: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Mathematics, 2022, vol. 11, issue 1, 1-25

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

Keywords: global existence; analyticity; decay estimate; hybrid Besov space; Navier–Stokes–Korteweg system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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