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Some remarks on the Navier-Stokes equations in \(\mathbf R^3\). (English) Zbl 0932.35166

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.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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