Regular time-reproductive solutions for generalized Boussinesq model with Neumann boundary conditions for temperature

Regular time-reproductive solutions for generalized Boussinesq model with Neumann boundary conditions for temperature Blanca Climent Ezquerra Francisco Guillén González Marko Rojas Medar Belem, julio 2006 1. Statement of the problem. The main result 2. The Galerkin Initial-Boundary Problem 3. Differential Inequalities in regular norms 4. Proof of theorem 5. Some comments and open problems 1. Statement of the problem 1. Statement of the problem 1. Statement of the problem Previous results: Existence and uniqueness of initial value problem with Dirichlet’s boundary conditions S.A. Lorca, J.L. Boldrini, Stationary solutions for generalized Boussinesq models, J. Diferential Equations 124 (2), (1996). Goal: To obtain strong estimates: for the velocity, for the temperature and consequently, existence of regular reproductive solution Difficulties: Time reproductive condition Nonlinear diffusion 1. Statement of the problem. Definition: 1. 1. Statement of the problem. 1. Statement of the problem. The main result 2. The Galerkin initial-boundary problem 4. Proof of theorem 4. Proof of theorem << T 4. Proof of theorem 4. Proof of theorem 4. Proof of theorem = = 5. Some comments and open problems