Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model

Abstract : 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.
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Submitted on : Thursday, August 10, 2017 - 3:06:25 PM
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Henri Gouin, Tommaso Ruggeri. Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model. Ricerche di matematica, Springer Verlag, 2017, 66 (2), pp.491-508. ⟨10.1007/s11587-016-0315-7⟩. ⟨hal-01573721⟩

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