Autor(es)

Chemetov, Nikolai, V ; Cipriano, Fernanda

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 57, n. 1, p. 40-pg., 2025-01-01.

Resumo

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 nonhomogeneous 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 Ga<^>\teaux 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. (AU)

• Processo FAPESP: 23/05271-4 - Problema de controlo ótimo através da fronteira para equações de Navier-Stokes estocásticas
• Beneficiário: Nikolai Vasilievich Chemetov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 21/03758-8 - Problemas matemáticos em dinâmica de fluidos
• Beneficiário: Nikolai Vasilievich Chemetov
• Modalidade de apoio: Auxílio à Pesquisa - Regular