Proof of Convergence of Iteration (1.25)

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 4 in Navier–Stokes Equations on R3 × [0, T], 2016, pp 33-35 from Springer

Abstract: Abstract We prove that if the initial vector u 0 belongs to the Banach space ℬ $$\mathcal{B}$$ defined in Definition 3.1.1 , then the iterative sequence of functions defined as in ( 1.25 ) converges to a unique solution for all T sufficiently small.

Keywords: Iterative Sequence; Unique Solution; Initial Vector; Contraction Mapping Principle; Partial Differential Equations (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-27526-0_4

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