Small Perturbations of Initial Conditions of Solutions of the Navier–Stokes Equations in the L3–Norm and Applications

Petr Kučera ()
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Petr Kučera: Czech Technical University, Department of Mathematics, Faculty of Civil Engineering

A chapter in Advances in Mathematical Fluid Mechanics, 2009, pp 319-328 from Springer

Abstract: Abstract In this paper, we solve two problems. We prove a theorem on stability of a strong solution with respect to the norm ║ ⋅ ║L2 +║⋅ ║L3 in Sect. 2. Then, in Sect.3, we show that there exist strong solutions of the Navier-Stokes initial-boundary value problem such that their initial values are arbitrarily large (in the norm of D(A¼)) and they belong to an arbitrarily chosen open set U ⊂ D(A½) at a time instant ξ > 0 which can be as small as we wish (We denote by A the Stokes operator.).

Keywords: Navier-Stokes equations; Stokes operator (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04068-9_20

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DOI: 10.1007/978-3-642-04068-9_20

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