A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems

• Published in: Archive for rational mechanics and analysis Vol. 220; no. 3; pp. 1095 - 1118
• Main Authors: Geissert, Matthias, Hieber, Matthias, Nguyen, Thieu Huy
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2016; Springer Nature B.V
• Subjects: Classical Mechanics; Complex Systems; Diffusion; Evolution; Flow control; Fluid dynamics; Fluid flow; Fluid- and Aerodynamics; Geophysics; Incompressible flow; Incompressible fluids; Interpolation; Mathematical analysis; Mathematical and Computational Physics; Navier-Stokes equations; Physics; Physics and Astronomy; Stokes flow; Theoretical; Viscous fluids; Periodic Solution; Mild Solution; Stokes Operator; Oseen Equation; Exterior Domain
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/s00205-015-0949-8

This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier–Stokes–Oseen flow, the Navier–Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein–Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.