Abstract
In this chapter we introduce some basic notions from the theory of the Navier–Stokes equations: the function spaces H, V, and V ′, the Stokes operator A with its domain D(A) in H, and the bilinear form B. We apply the Galerkin method and fixed point theorems to prove the existence of solutions of the nonlinear stationary problem, and we consider problems of uniqueness and regularity of solutions.
Now I think hydrodynamics is to be the root of all physical science, and is at present second to none in the beauty of its mathematics.
– William Thomson, 1st Baron Kelvin
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Łukaszewicz, G., Kalita, P. (2016). Stationary Solutions of the Navier–Stokes Equations. In: Navier–Stokes Equations. Advances in Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27760-8_4
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DOI: https://doi.org/10.1007/978-3-319-27760-8_4
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