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.
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Stenger, F., Tucker, D., Baumann, G. (2016). Spaces of Solution of the N–S Equations. In: Navier–Stokes Equations on R3 × [0, T]. Springer, Cham. https://doi.org/10.1007/978-3-319-27526-0_3
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DOI: https://doi.org/10.1007/978-3-319-27526-0_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27524-6
Online ISBN: 978-3-319-27526-0
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