The Stokes Equation in the L p -Setting: Well-Posedness and Regularity Properties

Matthias Hieber () and Jürgen Saal ()
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Matthias Hieber: Technische Universität Darmstadt, Angewandte Analysis, Fachbereich Mathematik
Jürgen Saal: Heinrich-Heine-Universität Düsseldorf, Mathematisches Institut

Chapter 3 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 117-206 from Springer

Abstract: Abstract This article discusses the Stokes equation in various classes of domains Ω ⊂ ℝ n $$\Omega \subset \mathbb{R}^{n}$$ within the L p -setting for 1 ≤ p ≤ ∞ from the point of view of evolution equations. Classical as well as modern approaches to well-posedness results for strong solutions to the Stokes equation, to the Helmholtz decomposition, to the Stokes semigroup, and to mixed maximal L q − L p -regularity results for 1 ¡ p, q

Keywords: Stokes equations; Helmholtz decomposition; Stokes semigroup; Maximal L p -regularity; L ∞ -estimates; L p − L q -smoothing (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13344-7_3

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DOI: 10.1007/978-3-319-13344-7_3

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