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On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83827

Title: On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
Authors: Cho, Yonggeun Browse this author
Kim, Hyunseok Browse this author
Keywords: classical solution
compressible Navier-Stokes equations
vacuum
Issue Date: 2004
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 676
Start Page: 1
End Page: 42
Abstract: We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain ­ of R3. We ¯rst prove the local existence of solutions (p u) in C([0; T*]; (p∞ +H3(Ω))×(D10 ∩ \D3)(Ω)) under the assumption that the data satis¯es a natural compatibility condition. Then deriving the smoothing effect of the velocity u in t > 0, we conclude that (p, u) is a classical solution in (0; T**) × Ω for some T** ∈ (0, T*]. For these results, the initial density needs not be bounded below away from zero and may vanish in an open subset (vacuum) of Ω.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69481
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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