Existence of strong solutions to the equations of unsteady motion of shear thickening incompressible fluids. (June 2015)

• Record Type: Journal Article
• Authors: Bae, Hyeong-Ohk; Wolf, Jörg
• Is Part Of: Nonlinear analysis. Volume 23(2015)
• Page Start: 160
• Page End: 182
• Publication Date: 2015-06
• Subjects: Shear thickening fluid -- Strong solution -- Weighted estimate -- Difference quotient -- Non-Newtonian fluid -- Short time regularity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.12.002
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We address the existence of strong solutions to a system of equations of motion of an incompressible non-Newtonian fluid. Our aim is to prove the short-time existence of strong solutions for the case of shear thickening viscosity, which corresponds to the power law ν ( D ) = ∣ D ∣ q − 2 ( 2 < q < + ∞ ) . In particular, we find that global strong solutions exist whenever q > 2.23 … . The results are obtained by flattening the boundary and by using the difference quotient method. Near the boundary, we use weighted estimates in the normal direction.