2024-03-28T16:13:43Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/144212022-11-17T02:08:08Zhdl_2115_20039hdl_2115_116On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densitiesCho, YonggeunKim, HyunseokClassical solutionCompressible Navier-Stokes equationsVacuum410We 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.SpringerJournal Articleapplication/pdfhttp://hdl.handle.net/2115/14421https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/14421/1/ManuscriptaMath_v120p91.pdf0025-26111432-1785manuscripta mathematica1201911292006-05enginfo:doi/10.1007/s00229-006-0637-yThe original publication is available at www.springerlink.comauthor