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- W2019936845 abstract "We are concerned with the existence and uniqueness of local or global solutions for slightly compressible viscous fluids in the whole space. In [6] and [7], we proved local and global well-posedness results for initial data in critical spaces very close to the one used by H. Fujita and T. Kato for incompressible flows (see [14]). In the present paper, we address the question of convergence to the incompressible model (for ill-prepared initial data) when the Mach number goes to zero. When the initial data are small in a critical space, we get global existence and convergence. For large initial data and a bit of additional regularity, the slightly compressible solution is shown to exist as long as the corresponding incompressible solution does. As a corollary, we get global existence (and uniqueness) for slightly compressible two-dimensional fluids. On étudie l'existence et l'unicité de solutions locales ou globales pour les fluides légèrement compressibles dans l'espace entier. Dans [6] et [7], on a montré que le modèle était bien posé dans des espaces critiques très proches de ceux utilisés par H. Fujita and T. Kato pour les fluides incompressibles (voir [14]). Dans cet article, on étudie la convergence vers le modèle incompressible (pour des données initiales mal préparées) lorsque le nombre de Mach tend vers zéro. On obtient un résultat d'existence et de convergence global en temps pour des données initiales petites et à régularité critique. Pour des données grandes mais un peu plus régulières, la solution du système légèrement compressible existe aussi longtemps que la solution incompressible correspondante. En particulier, on a existence (et unicité) globale en dimension deux pour les fluides légèrement compressibles." @default.
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- W2019936845 date "2002-01-01" @default.
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- W2019936845 title "Zero Mach number limit in critical spaces for compressible Navier–Stokes equations" @default.
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- W2019936845 doi "https://doi.org/10.1016/s0012-9593(01)01085-0" @default.
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