Local controllability to stationary trajectories of a one-dimensional simplified model arising in turbulence

Sorin Micu (1) , Takéo Takahashi (2, 3)

1 UCV - Department of Mathematics
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine

This article studies the local controllability totrajectories of a one dimensional model for turbulence.By linearization we are led to an equation with a non local termwhose controllability properties are analyzed by using Fourierdecomposition and biorthogonal techniques. Once the existence ofcontrols is proved and the dependence of their norms with respectto the time is established for the linearized model, a fixed pointmethod allows us to deduce the result for the nonlinear initialproblem.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Sorin Micu, Takéo Takahashi. Local controllability to stationary trajectories of a one-dimensional simplified model arising in turbulence. Journal of Differential Equations, 2018, ⟨10.1016/j.jde.2017.11.029⟩. ⟨hal-01572317⟩