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• W2963093742 abstract "In this paper, we get a result on global existence of classical and strong solutions of the full compressible Navier–Stokes equations in three space dimensions with spherically or cylindrically symmetric initial data which may be large. The appearance of vacuum is allowed. In particular, if the initial data is spherically symmetric, the space dimension can be taken not less than two. The analysis is based on some delicate a priori estimates globally in time which depend on the assumption κ=O(1+θq) where q>r (r can be zero), which relaxes the condition q⩾2+2r in [12], [27], [39]. This could be viewed as an extensive work of [16] where the equations hold in the sense of distributions in the set where the density is positive with initial data which is large, discontinuous, and spherically or cylindrically symmetric in three space dimension. Dans cet article on obtient un résultat d'existence globale de solutions classiques et fortes des équations de Navier–Stokes complètes en trois dimensions pour des fluides incomipressibles et pour de grandes données initiales, sphériques ou cylindriques et symétriqus. L'apparition de vide est possible. En particulier si les données initiales sont sphériques ou cylindriques la dimension de l'espace peut être choisie au moins égale à deux. L'analyse utilise des estimationns a priori délicates globales en temps et dépendant de l'hypothèse κ=O(1+θq) où q>r (r peut être égal à zéro), ce qui affaiblit la condition q⩾2+2r donnée dans [12], [27], [39]. Ce résultat peut être considéré comme une extension des résultats obtenus dans les travaux [16] où les équations ont des solutions distributions dans l'ensemble où la densité est positive et les données initiales sont grandes, discontinues, sphériques ou cylindriques et symétriques dans un espace à trois dimensions." @default.
• W2963093742 created "2019-07-30" @default.
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• W2963093742 date "2014-09-01" @default.
• W2963093742 modified "2023-10-17" @default.
• W2963093742 title "Global symmetric classical solutions of the full compressible Navier–Stokes equations with vacuum and large initial data" @default.
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• W2963093742 doi "https://doi.org/10.1016/j.matpur.2013.12.003" @default.
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