Gallagher, Isabelle A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations. (English) Zbl 0997.35050 J. Math. Kyoto Univ. 40, No. 3, 525-540 (2000). The author studies periodic solutions of the weakly compressible Navier-Stokes equations for small Mach numbers. The main results of the paper are: (i) If the initial velocity satisfies a smallness condition in terms of the viscosity, then the system has a smooth solution for all \(T > 0.\)(ii) As the Mach number tends to zero, the solution of the compressible system approaches the solution of the incompressible Navier-Stokes equations plus a term which represents the fast waves. Reviewer: Klaus Deckelnick (Brighton) Cited in 11 Documents MSC: 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35B10 Periodic solutions to PDEs Keywords:compressible Navier-Stokes equations; periodic solutions; Mach number; weakly compressible PDFBibTeX XMLCite \textit{I. Gallagher}, J. Math. Kyoto Univ. 40, No. 3, 525--540 (2000; Zbl 0997.35050) Full Text: DOI