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In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping…

Analysis of PDEs · Mathematics 2017-06-02 Varga K. Kalantarov , Edriss S. Titi

We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…

Analysis of PDEs · Mathematics 2019-01-08 Benjamin Melinand , Kevin Zumbrun

In this article we study the local stabilization of the non-homogeneous Navier- Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that…

Analysis of PDEs · Mathematics 2018-07-12 Sourav Mitra

We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…

Analysis of PDEs · Mathematics 2011-10-05 Armen Shirikyan

In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…

Analysis of PDEs · Mathematics 2022-10-24 Sakil Ahamed , Debanjana Mitra

The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…

Analysis of PDEs · Mathematics 2015-10-15 Wojciech Zajaczkowski

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…

Analysis of PDEs · Mathematics 2020-12-24 Marco Cannone , Grzegorz Karch , Dominika Pilarczyk , Gang Wu

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

Analysis of PDEs · Mathematics 2017-03-07 Jean-Michel Coron , Frédéric Marbach , Franck Sueur

We consider the 2D incompressible Navier-Stokes equation in a rectangle with the usual no-slip boundary condition prescribed on the upper and lower boundaries. We prove that for any positive time, for any finite energy initial data, there…

Analysis of PDEs · Mathematics 2019-10-30 Jean-Michel Coron , Frédéric Marbach , Franck Sueur , Ping Zhang

In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange…

Optimization and Control · Mathematics 2019-05-07 Exequiel Mallea-Zepeda , Elva Ortega-Torres , Élder J. Villamizar-Roa

In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…

Analysis of PDEs · Mathematics 2023-11-28 Jincheng Gao , Lianyun Peng , Zheng-an Yao

In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…

Analysis of PDEs · Mathematics 2007-05-23 Thomas Y. Hou , Congming Li

In this article, we study the null controllability of linearized compressible Navier-Stokes system in one and two dimension. We first study the one-dimensional compressible Navier-Stokes system for non-barotropic fluid linearized around a…

Optimization and Control · Mathematics 2016-04-19 Debayan Maity

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…

Analysis of PDEs · Mathematics 2014-06-04 Wojciech Zajączkowski , Ewa Zadrzyńska

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

Numerical Analysis · Mathematics 2025-04-16 Santolo Leveque , Michele Benzi , Patrick E. Farrell

The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on the whole boundary. Our study is then…

Analysis of PDEs · Mathematics 2015-12-22 Sylvain Ervedoza , Olivier Glass , Sergio Guerrero

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

Optimization and Control · Mathematics 2010-05-19 Hanbing Liu

We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove…

Analysis of PDEs · Mathematics 2017-06-01 Roger Lewandowski

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…

Analysis of PDEs · Mathematics 2014-04-08 Peter Bella , Eduard Feireisl , Bum Ja Jin , Antonin Novotny

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…

Analysis of PDEs · Mathematics 2007-06-13 Ting Zhang , Daoyuan Fang