1999/09/01 by Sergey Gavrilyuk, Tommaso Ruggeri, Henri Gouin · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Conservation law #Conservation of energy #Constant (computer programming) #Energy functional #Field (mathematics) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Hermitian matrix #Internal energy #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Property (philosophy) #Quantum mechanics #Thermodynamics #Van der Waals equation #cond-mat.stat-mech #math-ph #math.GM #math.MP #physics.flu-dyn #van der Waals force
paper · pdf · doi:10.1016/s0020-7225(98)00131-1
published as Ricerche di matematica, Springer Verlag, 37, pp.1495 (2017) · 28 pages
openalex publication_date 1999/09/01 · arxiv created 2017/08/11 · arxiv updated 2017/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals' one and other models associated with a second order expansion. The aim of the paper is to prove-with a fourth-gradient internal energy already obtained by the mean field theory-that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations' systems when an equation of energy associated with high order deformation of a continuum medium is taken into account.