arXiv subjects

Diego A. Rueda-Gómez

Publications and source records attributed to Diego A. Rueda-Gómez.

3 recordsLinked to original sources

arXiv2024

On the fractional heat semigroup and product estimates in Besov spaces and applications in theoretical analysis of the fractional Keller-Segel system

This paper is concerned with the fractional Keller-Segel system in the temporal and spatial variables. We consider fractional dissipation for the physical variables including a fractional dissipation mechanism for the chemotactic diffusion, as well as a time fractional variation assumed in the Caputo sense. We analyze the fractional heat semigroup obtaining time decay and integral estimates of the Mittag-Leffler operators in critical Besov spaces, and prove a bilinear estimate derived from the nonlinearity of the Keller-Segel system, without using auxiliary norms. We use these results in order to prove the existence of global solutions in critical homogeneous Besov spaces employing only the norm of the natural persistence space, including the existence of self-similar solutions, which constitutes a persistence result in this framework. In addition, we prove a uniqueness result without assuming any smallness condition of the initial data.

math.AP↗

arXiv2019

Numerical analysis for a chemotaxis-Navier-Stokes system

In this paper we develop a numerical scheme for approximating a $d$-dimensional chemotaxis-Navier-Stokes system, $d=2,3$, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases where the chemical signal is consumed with a rate proportional to the amount of organisms. We construct numerical approximations based on the Finite Element method and analyze some error estimates and convergence towards weak solutions. In order to construct the numerical scheme, we use a splitting technique to deal with the chemo-attraction term in the cell-density equation, leading to introduce a new variable given by the gradient of the chemical concentration. Having the equivalent model, we consider a fully discrete Finite Element approximation which is well-posed and it is mass-conservative. We obtain uniform estimates and analyze the convergence of the scheme. Finally, we present some numerical simulations to verify the good behavior of our scheme, as well as to check numerically the error estimates proved in our theoretical analysis.

math.NA↗

arXiv2016

A boundary control problem associated to the Rayleigh-Bénard-Marangoni system

In this paper, we study a boundary control problem associated to the stationary Rayleigh-Bénard-Marangoni (RBM) system in presence of controls for the velocity and the temperature on parts of the boundary. We analyze the existence, uniqueness and regularity of weak solutions for the stationary RBM system in polyhedral domains of $\mathbb{R}^3,$ and then, we prove the existence of the optimal solution. By using the Theorem of Lagrange multipliers, we derive an optimality system. We also give a second-order sufficient optimality condition and we establish a result of uniqueness of the optimal solution.

math.AP↗