Symmetrization and local existence of strong solutions for diffuse interface fluid models - Archive ouverte HAL
Article Dans Une Revue Journal of Mathematical Fluid Mechanics Année : 2023

Symmetrization and local existence of strong solutions for diffuse interface fluid models

Résumé

We investigate compressible nonisothermal diffuse interface fluid models also termed capillary fluids. Such fluid models involve van der Waals' gradient energy, Korteweg's tensor, Dunn and Serrin's heat flux as well as diffusive fluxes. The density gradient is added as an extra variable and the convective and capillary fluxes of the augmented system are identified by using the Legendre transform of entropy. The augmented system of equations is recast into a normal form with symmetric hyperbolic first order terms, symmetric dissipative second order terms and antisymmetric capillary second order terms. New a priori estimates are obtained for such augmented system of equations in normal form. The time derivatives of the parabolic components are less regular than for standard hyperbolic-parabolic systems and the strongly coupling antisymmetric fluxes yields new majorizing terms. Using the augmented system in normal form and the a priori estimates, local existence of strong solutions is established in an Hilbertian framework.
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Dates et versions

hal-03841943 , version 1 (07-11-2022)

Identifiants

Citer

Vincent Giovangigli, Yoann Le Calvez, Flore Nabet. Symmetrization and local existence of strong solutions for diffuse interface fluid models. Journal of Mathematical Fluid Mechanics, 2023, 25 (4), pp.82. ⟨10.1007/s00021-023-00825-4⟩. ⟨hal-03841943⟩
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