Abstract
In this paper the homogeneous, incompressible Navier-Stokes equations are considered, and a number of results are reviewed which are related to the scaling of the equations. More specifically the initial value problem is studied in scale-invariant function spaces, insisting on the special role of the “largest” scale-invariant function space; the specificity of two space dimensions is recalled, in terms of the velocity field and the vorticity. Some examples of arbitrarily large initial data giving rise to a global solution are also provided, as well as a study of the long-time behavior of global solutions and their behavior at blow-up time (supposing such a time exists).
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Gallagher, I. (2018). Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_12
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