Spaces of Solution of the N–S Equations

Frank Stenger, Don Tucker and Gerd Baumann
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Frank Stenger: University of Utah, School of Computing
Don Tucker: University of Utah, Department of Mathematics
Gerd Baumann: German University in Cairo, Department of Mathematics

Chapter Chapter 3 in Navier–Stokes Equations on R3 × [0, T], 2016, pp 19-31 from Springer

Abstract: Abstract In this chapter we prove that if each component of the vector u on the right-hand side of (1.11) is divergence-free and belongs to the space of functions A α, d, T 3, then the same is true of the operation N u on the right-hand side of (1.11). We also derive some bilinear form expressions for the operation N u thus paving the way for our proof of existence of a solution to (1.11). We then give precise conditions for convergence of successive approximations to the solution of (1.11) based on the contraction mapping principle.

Keywords: Contraction Mapping Principle; Right-hand Side; Bilinear Form; Bilinear Operation; Asymptotic Relation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-27526-0_3

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DOI: 10.1007/978-3-319-27526-0_3

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