Feedback control for fluid mixing via advection
DOI10.1016/j.jde.2023.07.009zbMath1527.35286MaRDI QIDQ6094875
Xiaoming Zheng, Carlos N. Rautenberg, Weiwei Hu
Publication date: 11 October 2023
Published in: Journal of Differential Equations (Search for Journal in Brave)
asymptotic behaviortransport equationnonlinear feedback controlStokes equationsinstantaneous controlfluid mixing
Optimality conditions for problems involving partial differential equations (49K20) Feedback control (93B52) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Turbulent transport, mixing (76F25) Existence theories for optimal control problems involving partial differential equations (49J20) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs in connection with control and optimization (35Q93) Transport equations (35Q49)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the attractor for the semi-dissipative Boussinesq equations
- Model predictive control: Theory and practice - a survey
- Control of mixing by boundary feedback in 2D channel flow.
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- Analysis of instantaneous control for the Burgers equation
- Boundary control for optimal mixing by Stokes flows
- Instantaneous control of backward-facing step flows
- Quantification of mixing in aperiodic chaotic flows
- Partially dissipative 2D Boussinesq equations with Navier type boundary conditions
- Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion
- Long time behavior of solutions to the 2D Boussinesq equations with zero diffusivity
- Stability and large-time behavior of the 2D Boussinesq equations with partial dissipation
- Polynomial mixing under a certain stationary Euler flow
- An approximating approach for boundary control of optimal mixing via Navier-Stokes flows
- Universal mixers in all dimensions
- Global regularity and long-time behavior of the solutions to the 2D Boussinesq equations without diffusivity in a bounded domain
- Mixing and un-mixing by incompressible flows
- A lemma and a conjecture on the cost of rearrangements
- A multiscale measure for mixing
- A framework for robustness analysis of constrained finite receding horizon control
- Fast Solution of Optimal Control Problems in the Selective Cooling of Steel
- DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms
- On the Stabilizability of the Burgers Equation by Receding Horizon Control
- Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows
- Optimal stirring strategies for passive scalar mixing
- Convexity and Optimization in Banach Spaces
- Using multiscale norms to quantify mixing and transport
- Feedback control for unsteady flow and its application to the stochastic Burgers equation
- Boundary Control for Optimal Mixing via Navier--Stokes Flows
- Optimization with PDE Constraints
- Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems
- Towards the design of an optimal mixer
- Nonlinear Schrödinger evolution equations
- The stability of constrained receding horizon control
- Suboptimal control of turbulent channel flow for drag reduction
- Suboptimal feedback control of vortex shedding at low Reynolds numbers
- Passive Scalars in Turbulent Flows
- Exponential self-similar mixing by incompressible flows
- The effect of the terminal penalty in Receding Horizon Control for a class of stabilization problems
- Foundations of chaotic mixing
- Maximal mixing by incompressible fluid flows
- On the regularity for the Boussinesq equations in a bounded domain
- Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows
