𝐿^{𝑝}-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids

Geissert, Matthias; Götze, Karoline; Hieber, Matthias

doi:10.1090/S0002-9947-2012-05652-2

$L^{p}$-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
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by Matthias Geissert, Karoline Götze and Matthias Hieber PDF

Trans. Amer. Math. Soc. 365 (2013), 1393-1439 Request permission

Abstract:

Consider the system of equations describing the motion of a rigid body immersed in a viscous, incompressible fluid of Newtonian or generalized Newtonian type. The class of fluids considered includes in particular shear-thinning or shear-thickening fluids of power-law type of exponent $d\geq 1$. We develop a method to prove that this system admits a unique, local, strong solution in the $L^p$-setting. The approach presented in the case of generalized Newtonian fluids is based on the theory of quasi-linear evolution equations and requires that the exponent $p$ satisfies the condition $p>5$.

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