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# High regularity of solutions of compressible Navier-Stokes equations

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 Please use this identifier to cite or link to this item:https://doi.org/10.14943/83926

 Title: High regularity of solutions of compressible Navier-Stokes equations Authors: Cho, Yonggeun Browse this author Keywords: viscous compressible fluids compressible Navier-Stokes equations vacuum Issue Date: 2006 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 776 Start Page: 1 End Page: 64 Abstract: We study the Navier-Stokes equations for compressible {\it barotropic} fluids in a bounded or unbounded domain $\Omega$ of $\mathbf{R}^3$. The initial density may vanish in an open subset of $\Omega$ or to be positive but vanish at space infinity. We first prove the local existence of solutions $(\rho^{(j)}, u^{(j)})$ in $C([0,T_* ]; H^{2(k-j)+3} \times D_0^1 \cap D^{2(k-j)+3} (\Omega ) )$, $0 \le j \le k, k \ge 1$ under the assumptions that the data satisfy compatibility conditions and that the initial density is sufficiently small. To control the nonnegativity or decay at infinity of density, we need to establish a boundary value problem of $(k+1)$-coupled elliptic system which may not be in general solvable. The smallness condition of initial density is necessary for the solvability, which is not necessary in case that the initial density has positive lower bound. Secondly, we prove the global existence of smooth radial solutions of {\it isentropic} compressible Navier-Stokes equations on a bounded annulus or a domain which is the exterior of a ball under a smallness condition of initial density. Type: bulletin (article) URI: http://hdl.handle.net/2115/69584 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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