arXiv subjects
Publications and source records attributed to Elva Ortega-Torres.
We prove new regularity criteria of the Prodi-Serrin type with weak Lebesgue integrability in both space and time for a viscous active chemical fluid in a bounded domain.
We study the existence of reproductive weak solutions for a system of equations describing a solidification process of a binary alloy confined into a bounded and regular domain in $\mathbb{R}^3$, having mixed boundary conditions.
In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$α$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange multipliers Theorem. Finally, considering a velocity tracking control problem for the three-dimensional Navier-Stokes-$α$ model, we analyze the relation of its optimality system to the corresponding one associated to the Navier-Stokes model by proving a convergence theorem, which establishes that, as the length scale $α$ goes to zero, the optimality system of the three-dimensional Navier-Stokes-$α$ model converges to the optimality system associated with the velocity tracking control problem of the Navier-Stokes equations.
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation of particles, on parts of the boundary of the flow domain. On the remaining part of the boundary, we consider mixed boundary conditions for the vector velocity (Dirichlet and Navier conditions) and Dirichlet boundary conditions for the angular velocity. We analyze the existence of a weak solution obtaining the fluid density as a scalar function of the stream function. We prove the existence of an optimal solution and, by using the Lagrange multipliers theorem, we state first-order optimality conditions. We also derive, through a penalty method, some optimality conditions satisfied by the optimal controls.
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are estab- lished. Moreover, by using the Lagrange multipliers method, an optimality system in a weak and a strong form is derived.