Two-dimensional equilibrium configurations in Korteweg fluids

M. Gorgone^a, F. Oliveri^a, A. Ricciardello^b, P. Rogolino<sup>a

a</sup> Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Messina, Italy
^b Faculty of Engineering and Architecture, Kore University of Enna, Cittadella Universitaria, Enna, Italy

Abstract: In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two-dimensional setting, it is derived a single nonlinear elliptic equation such that the equilibrium conditions are identically satisfied. Such an equation is discussed both analytically and numerically. Moreover, by considering a particular boundary value problem of Dirichlet type, some preliminary numerical solutions are presented.

Keywords: Korteweg fluids, equilibrium configurations.

MSC: Primary 76-10; Secondary 76A10; 76M20

Received: 30.09.2022
Revised: 28.10.2022

Language: English

DOI: 10.2298/TAM220930008G