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

Cho, Yonggeun; Kim, Hyunseok

Hokkaido University Preprint Series in Mathematics, 2004, 676, 1-42

Permalink : https://doi.org/10.14943/83827

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DOI	https://doi.org/10.14943/83827
URI	https://hdl.handle.net/2115/69481
タイトル	On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
著者	著者名 Cho, Yonggeun
著者	著者名 Kim, Hyunseok
言語	英語
キーワード	classical solution
	compressible Navier-Stokes equations
	vacuum
発行日	2004
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	676
ページ	1-42
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record