arXiv subjects

P. Braz e Silva

Publications and source records attributed to P. Braz e Silva.

4 recordsLinked to original sources

arXiv2022

Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains

An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary optimality system are deduced. The main novelty is that control can be rather singular and the state (cell density $u$ and the chemical concentration $v$) remains only in a weak setting, which is not usual in the literature to solve optimal control problems subject to chemotaxis models (see e.g. Guillén-González et al. ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 29, 21 pp).

math.OC↗

arXiv2022

High order asymptotic inequalities for some dissipative systems

We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been observed in the literature even for the fundamental Navier-Stokes equations.To illustrate this new approach, we derive bounds for the asymmetric incompressible fluids equations, where an improved inequalities established for the micro-rotational field. Finally, we show how this technique can be applied for other dissipative systems.

math.AP↗

arXiv2007

On the existence of infinite energy solutions for nonlinear Schrodinger equations

We derive new results about existence and uniqueness of local and global solutions for nonlinear Schrodinger equation, including self-similar global solutions. Our analysis is performed in the framework of Marcinkiewicz spaces.

math.AP↗

arXiv2006

Error bounds for semi-Galerkin approximations of nonhomogeneous incompressible fluids

We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the $H^1$ norm for the velocity. We also derive an error estimate for the density in some spaces $L^r$.

math.AP↗