2024-03-28T19:57:35Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694812022-11-17T02:08:08Zhdl_2115_45007hdl_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 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69481info:doi/10.14943/83827https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69481/1/pre676.pdfHokkaido University Preprint Series in Mathematics6761422004engpublisher