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On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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