11,741 research outputs found
The viscous surface-internal wave problem: global well-posedness and decay
We consider the free boundary problem for two layers of immiscible, viscous,
incompressible fluid in a uniform gravitational field, lying above a general
rigid bottom in a three-dimensional horizontally periodic setting. We establish
the global well-posedness of the problem both with and without surface tension.
We prove that without surface tension the solution decays to the equilibrium
state at an almost exponential rate; with surface tension, we show that the
solution decays at an exponential rate. Our results include the case in which a
heavier fluid lies above a lighter one, provided that the surface tension at
the free internal interface is above a critical value, which we identify. This
means that sufficiently large surface tension stabilizes the Rayleigh-Taylor
instability in the nonlinear setting. As a part of our analysis, we establish
elliptic estimates for the two-phase stationary Stokes problem.Comment: 70 pages; v2: typos and minor errors correcte
A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control
Gain-scheduled control based on linear parameter-varying (LPV) models derived
from local linearizations is a widespread nonlinear technique for tracking
time-varying setpoints. Recently, a nonlinear control scheme based on Control
Contraction Metrics (CCMs) has been developed to track arbitrary admissible
trajectories. This paper presents a comparison study of these two approaches.
We show that the CCM based approach is an extended gain-scheduled control
scheme which achieves global reference-independent stability and performance
through an exact control realization which integrates a series of local LPV
controllers on a particular path between the current and reference states.Comment: IFAC LPVS 201
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