Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
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: | 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)
|