arXiv subjects

Nikolai Chemetov

Publications and source records attributed to Nikolai Chemetov.

5 recordsLinked to original sources

arXiv2024

Optimal control of Newtonian fluids in a stochastic environment

We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the non-homogeneous Navier-slip boundary conditions. After establishing a suitable stability result for the solution of the stochastic state equation, we prove the well-posedness of the stochastic linearized state equation and show that the Gâteaux derivative of the control-to-state mapping corresponds to the unique solution of the linearized equation. Next, we study the stochastic backward adjoint equation and establish a duality relation between the solutions of the forward linearized equation and the backward adjoint equation. Finally, we derive the first-order optimality conditions.

math.PR↗

arXiv2023

Boundary control problem for stochastic 2d-Navier-Stokes equations

We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty, modeled by stochastic non-homogeneous Navier-slip boundary conditions. We show the existence and uniqueness of the solution to the state equation, and prove the existence of an optimal solution to the control problem.

math.AP↗

arXiv2017

Optimal control for two-dimensional stochastic second grade fluids

This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition.

math.AP↗

arXiv2017

Well-posedness of stochastic second grade fluids

The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study stochastic second grade fluids filling a two-dimensional bounded domain, with the Navier-slip boundary condition (with friction). We prove the well-posedness of this problem and establish a stability result. Our stochastic model involves a multiplicative white noise and a convective term with third order derivatives, which significantly complicate the analysis.

math.AP↗

arXiv2010

The generalized Buckley-Leverett System. Solvability

We propose a new approach to the mathematical modeling of the Buckley- Leverett system, which describes two-phase flows in porous media. Considering the initial-boundary value problem for a deduced model, we prove the solvability of the problem. The solvability result relies mostly on the kinetic method.

math.AP↗