Cleyton Cunha - UFPE/UFPI

Título:

A Study of the Initialization Problem for the Equations of Incompressible Asymmetric Fluids.

Resumo:

In this talk we approached the initialization problem for the asymmetric (micropolar) incompressible fluids equations in domains of R^2. This kind of problem is of great importance in meteorological studies, as for example in numerical weather prediction, and more generally in many other types of numerical simulations for prediction models. We use techniques of optimal control following the ideas from [1, 2, 3]. We prove that this problem has at least one and at most finite many of solutions. Finally, we determine conditions that imply at uniqueness of solution.

References:

[1] Notte-Cuello, E.; Rojas-Medar, M. A.; Santos, M., A study of the initialization problem for the magnetohydrodynamic type equations. In: J.M. Balthazar, P.B. Gonçalnez, R.M.F.L.F. Brasil, I.L. Caldas, F. B. Rizatto. (Org.). Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences. 1ed., 2002, v. 6, p. 39-49.

[2] Zhou, J., A Study of the Initialization Problem for the Navier-Stoke Equations, J. Math. Anal. and Applications 190, 678-696, 1995.

[3] White, l. W., A Study of Uniqueness for the Initialization Problem for Burger’s Equation, J. Math. Anal. Appl. 172, 412-431, 1993.