Global Stabilization of the Navier-Stokes Equations Around an Unstable Steady State with Mixed Boundary Kinetic Energy Controller View Full Text


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Article Info

DATE

2019-04

AUTHORS

Abdou Sène, Timack Ngom, Evrad M. D. Ngom

ABSTRACT

The paper, benefiting from techniques developed in Ngom et al. (Evol Equ Control Theory. 2015;4:89–106), presents a mixed (Dirichlet-Neumann) boundary feedback controller for stabilizing the Navier-Stokes equations around a prescribed steady state, in a bounded domain Ω. The Neumann part of the boundary controller is designed to be zero when the inflow vanishes, and to have the magnitude of the kinetic energy. Like in Ngom et al. (Evol Equ Control Theory. 2015;4:89–106), the present paper proves exponential decrease of the perturbation in L2, without blowup. In addition, it goes further than (Ngom et al., Evol Equ Control Theory. 2015;4:89–106) by proving, on the one hand, that the exponential convergence towards zero holds in H1, on the other hand, that the weak solution is unique when the computational domainis two-dimensional. More... »

PAGES

197-218

References to SciGraph publications

  • 2013-09. Control of shallow water and sediment continuity coupled system in MATHEMATICS OF CONTROL, SIGNALS, AND SYSTEMS
  • 2001-09. Stabilizability of Two-Dimensional Navier—Stokes Equations with Help of a Boundary Feedback Control in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 1998-12. Local Solutions to the Navier–Stokes Equations with Mixed Boundary Conditions in ACTA APPLICANDAE MATHEMATICAE
  • 2014-12. On the Sobolev trace Theorem for variable exponent spaces in the critical range in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 2013-12. A delayed feedback control for network of open canals in INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL
  • 2007. Local Exponential Stabilization Strategies of the Navier-Stokes Equations, d = 2, 3, via Feedback Stabilization of its Linearization in CONTROL OF COUPLED PARTIAL DIFFERENTIAL EQUATIONS
  • 2000. Optimal Control Problems for the Navier-Stokes Equations in LECTURES ON APPLIED MATHEMATICS
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