Optimal boundary control problem for stochastic Navier-Stokes equations

• Grant number: 23/05271-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 09, 2023
• End date: July 22, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Nikolai Vasilievich Chemetov
• Grantee: Nikolai Vasilievich Chemetov
• Visiting researcher: Maria Fernanda de Almeida Cipriano Salvador Marques
• Visiting researcher institution: Universidade Nova de Lisboa, Portugal
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

A boundary control is of main importance in several branches of the industry, providing design and modeling optimal capability for diverse products such as jet engines, pumps, food production and vacuum cleaners.In this project we consider a velocity tracking problem for the Navier-Stokes equations in a bounded domain. The control acts on the boundary through an injection-suction device and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.During this visit, a joint research work will be carried out by Professor Nikolai Chemetov (host) with Visiting Professor Fernanda Cipriano, from the New University of Lisbon, Portugal, on a mathematical model related with the control problem of Newtonian fluid through boundary conditions.In addition, Professor Fernanda Cipriano will be the organizing member of the "Stochastic Processes" session of the 14th International ISAAC Congress and give a lecture on stochastic mathematical models in Fluid Mechanics at this session. (AU)