A Note on the Cauchy Problem for the Navier–Stokes Equations

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Previous article Next article A Note on the Cauchy Problem for the Navier–Stokes EquationsJ. R. Cannon and George H. KnightlyJ. R. Cannon and George H. Knightlyhttps://doi.org/10.1137/0118056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. R. Cannon and , George H. Knightly, Some continuous dependence theorems for viscous fluid motions, SIAM J. Appl. Math., 18 (1970), 627–640 10.1137/0118055 MR0269967 (42:4860) 0202.37202 LinkISIGoogle Scholar[2] Robert Finn, On the Stokes Paradox and related questions, Nonlinear Problems (Proc. Sympos., Madison, Wis., 1962), Univ. of Wisconsin Press, Madison, Wis., 1963, 99–115 MR0152764 (27:2739) 0115.20902 Google Scholar[3] M. Gevrey, Sur les équations aux derivées partielles du type parabolique, J. Math. Puees Appl. (6), 9 (1913), 305–471 Google Scholar[4] Charles Kahane, On the spatial analyticity of solutions of the Navier-Stokes equations., Arch. Rational Mech. Anal., 33 (1969), 386–405 10.1007/BF00247697 MR0245989 (39:7295) 0186.16801 CrossrefISIGoogle Scholar[5] George H. Knightly, On a class of global solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 21 (1966), 211–245 10.1007/BF00253489 MR0191213 (32:8621) 0148.21603 CrossrefISIGoogle Scholar[6] Kyûya Masuda, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation, Proc. Japan Acad., 43 (1967), 827–832 MR0247304 (40:572) 0204.26901 CrossrefGoogle Scholar[7] C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Akadamische Verlagsgesellschaft, Leipzig, 1927 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Maximum Norm Estimates of the Solution of the Navier-Stokes Equations in the Halfspace with Bounded Initial DataAbstract and Applied Analysis, Vol. 2021 | 16 Feb 2021 Cross Ref Time Analyticity for Inhomogeneous Parabolic Equations and the Navier–Stokes Equations in the Half SpaceJournal of Mathematical Fluid Mechanics, Vol. 22, No. 4 | 4 September 2020 Cross Ref Time analyticity for the heat equation and Navier-Stokes equationsJournal of Functional Analysis, Vol. 279, No. 4 | 1 Sep 2020 Cross Ref Exterior Navier-Stokes flows for bounded dataMathematische Nachrichten, Vol. 290, No. 7 | 22 September 2016 Cross Ref BibliographyThe Navier-Stokes Problem in the 21st Century | 3 March 2016 Cross Ref The Navier–Stokes Equations in a Space of Bounded FunctionsCommunications in Mathematical Physics, Vol. 338, No. 2 | 16 April 2015 Cross Ref Non-Decaying Solutions to the Navier Stokes Equations in Exterior DomainsActa Applicandae Mathematicae, Vol. 132, No. 1 | 27 May 2014 Cross Ref Well-posedness of the Stokes–Coriolis system in the half-space over a rough surfaceAnalysis & PDE, Vol. 7, No. 6 | 18 October 2014 Cross Ref The Navier–Stokes flow around the linearly growing steady state with bounded disturbanceANNALI DELL'UNIVERSITA' DI FERRARA, Vol. 55, No. 2 | 29 September 2009 Cross Ref Stokes and Navier–Stokes problems in a half-space: the existence and uniqueness of solutions a priori nonconvergent to a limit at infinityJournal of Mathematical Sciences, Vol. 159, No. 4 | 29 May 2009 Cross Ref On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on L∞Journal of Differential Equations, Vol. 246, No. 7 | 1 Apr 2009 Cross Ref Remarks on Global Solvability of 2-D Boussinesq Equations with Non-Decaying Initial DataFunkcialaj Ekvacioj, Vol. 49, No. 1 | 1 Jan 2006 Cross Ref A priori estimates in terms of the maximum norm for the solutions of the Navier–Stokes equationsJournal of Differential Equations, Vol. 203, No. 2 | 1 Sep 2004 Cross Ref Uniformly Local L p Estimate for 2-D Vorticity Equation and Its Application to Euler Equations with Initial Vorticity in bmoCommunications in Mathematical Physics, Vol. 248, No. 1 | 7 May 2004 Cross Ref On the Boussinesq Flow with Nondecaying Initial DataFunkcialaj Ekvacioj, Vol. 47, No. 2 | 1 Jan 2004 Cross Ref On the uniqueness of viscous fluid motionsArchive for Rational Mechanics and Analysis, Vol. 62, No. 3 | 1 Sep 1976 Cross Ref A Cauchy Problem for the Navier-Stokes Equations in $R^n$George H. KnightlySIAM Journal on Mathematical Analysis, Vol. 3, No. 3 | 17 February 2012AbstractPDF (559 KB)Some Continuous Dependence Theorems for Viscous Fluid MotionsJ. R. Cannon and George H. KnightlySIAM Journal on Applied Mathematics, Vol. 18, No. 3 | 1 August 2006AbstractPDF (1129 KB) Volume 18, Issue 3| 1970SIAM Journal on Applied Mathematics539-719 History Submitted:20 May 1969Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118056Article page range:pp. 641-644ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics