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

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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: May-2006
Publisher: Springer
Journal Title: manuscripta mathematica
Volume: 120
Issue: 1
Start Page: 91
End Page: 129
Publisher DOI: 10.1007/s00229-006-0637-y
Abstract: We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Ω of R^3. We first prove the local existence of solutions (ρ,u) in C([0,T_*]; (ρ^∞ + H^3(Ω)) × D^1_0 ∩ D^3)(Ω)) under the assumption that the data satisfies a natural compatibility condition. Then deriving the smoothing effect of the velocity u in t > 0, we conclude that (ρ,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.
Rights: The original publication is available at www.springerlink.com
Type: article (author version)
URI: http://hdl.handle.net/2115/14421
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 趙 庸根 (Cho, Yonggeun)

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