2020/04/25 by Giada Cianfarani Carnevale, Carnevale, Giada Cianfarani, Corrado Lattanzio +1 · 1 citation
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2004.12241
openalex publication_date 2020/04/25 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28
The aim of this paper is to investigate the singular relaxation limits for\nthe Euler-Korteweg and the Navier-Stokes-Korteweg system in the high friction\nregime. We shall prove that the viscosity term is present only in higher orders\nin the proposed scaling and therefore it does not affect the limiting dynamics,\nand the two models share the same equilibrium equation. The analysis of the\nlimit is carried out using the relative entropy techniques in the framework of\nweak, finite energy solutions of the relaxation models converging toward smooth\nsolutions of the equilibrium. The results proved here take advantage of the\nenlarged formulation of the models in terms of the drift velocity introduced in\n[6], generalizing in this way the ones proved in [15] for the Euler-Korteweg\nmodel.\n