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Spaces of Solution of the N–S Equations

In: Navier–Stokes Equations on R3 × [0, T]

Author

Listed:
  • 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
    University of Ulm)

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.

Suggested Citation

  • Frank Stenger & Don Tucker & Gerd Baumann, 2016. "Spaces of Solution of the N–S Equations," Springer Books, in: Navier–Stokes Equations on R3 × [0, T], chapter 0, pages 19-31, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-27526-0_3
    DOI: 10.1007/978-3-319-27526-0_3
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