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Keywords = hybrid Besov space

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28 pages, 400 KiB  
Article
Global Analysis of Compressible Navier–Stokes–Korteweg Equations: Well-Posedness and Gevrey Analyticity
by Jianzhong Zhang, Weixuan Shi and Minggang Han
Axioms 2025, 14(6), 411; https://doi.org/10.3390/axioms14060411 - 28 May 2025
Viewed by 268
Abstract
This paper investigates the Cauchy problem for the full compressible Navier–Stokes–Korteweg equations, which model fluid dynamics with capillary properties in Rd(d3). And the global well-posedness and Gevrey analytic of strong solutions for the system are established [...] Read more.
This paper investigates the Cauchy problem for the full compressible Navier–Stokes–Korteweg equations, which model fluid dynamics with capillary properties in Rd(d3). And the global well-posedness and Gevrey analytic of strong solutions for the system are established in the L2Lp type critical hybrid Besov space with 2p2dd2 and p<d. Full article
25 pages, 388 KiB  
Article
Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces
by Zihao Song and Jiang Xu
Mathematics 2023, 11(1), 174; https://doi.org/10.3390/math11010174 - 29 Dec 2022
Viewed by 1523
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 [...] Read more.
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. Full article
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