TY - JOUR
T1 - Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
AU - Geissert, Matthias
AU - Götze, Karoline
AU - Hieber, Matthias Georg
PY - 2013
Y1 - 2013
N2 - 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 shearthinning or shear-thickening fluids of power-law type of exponent d ≥ 1. We develop a method to prove that this system admits a unique, local, strong solution in the Lp-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.
AB - 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 shearthinning or shear-thickening fluids of power-law type of exponent d ≥ 1. We develop a method to prove that this system admits a unique, local, strong solution in the Lp-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.
KW - Fluid-rigid body interaction
KW - Generalized Newtonian fluids
KW - Strong L-solutions
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U2 - 10.1090/S0002-9947-2012-05652-2
DO - 10.1090/S0002-9947-2012-05652-2
M3 - Article
AN - SCOPUS:84871579393
VL - 365
SP - 1393
EP - 1439
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 3
ER -