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Pré-Publication, Document De Travail Année : 2024

Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density

Résumé

We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as blocks, for \textit{less} regular initial data where the vacuum is permitted, the global-in-time well-posedness follows from the energy estimates and the propagated striated regularity of the density function, if the bulk viscosity coefficient is large enough in the two dimensional case. The global-in-time well-posedness holds also true in the three dimensional case, provided with large bulk viscosity coefficient together with small initial energy. This solves the density-patch problem in the exterior domain for the compressible model with $W^{2,p}$-Interfaces. Finally, the singular incompressible limit toward the inhomogenous incompressible model when the bulk viscosity coefficient tends to infinity is obtained.
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hal-04586708 , version 1 (24-05-2024)

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Xian Liao, Sagbo Marcel Zodji. Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density. 2024. ⟨hal-04586708⟩
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