Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem

Isabelle Gallagher ()
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Isabelle Gallagher: Paris-Diderot University, Department of Mathematics

Chapter 12 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 647-685 from Springer

Abstract: 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).

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_12

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DOI: 10.1007/978-3-319-13344-7_12

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