Lemarié-Rieusset, Pierre Gilles Some remarks on the Navier-Stokes equations in \(\mathbf R^3\). (English) Zbl 0932.35166 J. Math. Phys. 39, No. 8, 4108-4118 (1998). We study various existence and uniqueness results for solutions of the Navier-Stokes equations in connection with function spaces related to real harmonic analysis. We are mainly interested in reviewing recent results concerning weak solutions of the Navier-Stokes equations which belongs to \({\mathcal C}([0,+\infty), L^2(\mathbb{R}^3))\). Such solutions were first studied by Kato in 1984. \(L^3\) estimates have been used as well in the study of Leray’s weak solutions, leading to the uniqueness theorem of Sohr and Von Wahl. Cited in 7 Documents MSC: 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids Keywords:existence; uniqueness; weak solutions of the Navier-Stokes equations PDFBibTeX XMLCite \textit{P. G. Lemarié-Rieusset}, J. Math. Phys. 39, No. 8, 4108--4118 (1998; Zbl 0932.35166) Full Text: DOI References: [1] DOI: 10.1007/BF01174182 · Zbl 0545.35073 · doi:10.1007/BF01174182 [2] DOI: 10.1007/BF02097391 · Zbl 0795.35080 · doi:10.1007/BF02097391 [3] DOI: 10.1016/S0764-4442(97)86952-2 · Zbl 0876.35083 · doi:10.1016/S0764-4442(97)86952-2 [4] DOI: 10.1007/BF02547354 · JFM 60.0726.05 · doi:10.1007/BF02547354 [5] DOI: 10.1007/BF00276188 · Zbl 0126.42301 · doi:10.1007/BF00276188 [6] DOI: 10.1007/BF01232939 · Zbl 0781.35052 · doi:10.1007/BF01232939 [7] DOI: 10.1080/03605309408821042 · Zbl 0803.35068 · doi:10.1080/03605309408821042 [8] DOI: 10.1080/03605309208820892 · Zbl 0771.35047 · doi:10.1080/03605309208820892 [9] DOI: 10.1080/03605308908820621 · Zbl 0681.35072 · doi:10.1080/03605308908820621 [10] DOI: 10.1002/cpa.3160350604 · Zbl 0509.35067 · doi:10.1002/cpa.3160350604 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.