arXiv subjects

Maicon J. Benvenutti

Publications and source records attributed to Maicon J. Benvenutti.

3 recordsLinked to original sources

arXiv2024

Parameter Error Analysis for the 3D Modified Leray-alpha Model: Analytical and Numerical Approaches

In this study, we conduct a parameter error analysis for the 3D modified Leray-$α$ model using both analytical and numerical approaches. We first prove the global well-posedness and continuous dependence of initial data for the assimilated system. Furthermore, given sufficient conditions on the physical parameters and norms of the true solution, we demonstrate that the true solution can be recovered from the approximation solution, with an error determined by the discrepancy between the true and approximating parameters. Numerical simulations are provided to validate the convergence criteria.

math.NA↗

arXiv2022

Parameter analysis in continuous data assimilation for three-dimensional Brinkman-Forchheimer-extended Darcy

In this paper, we study analytically the long-time behavior of three-dimensional Brinkman-Forchheimer-extended Darcy model, in the context that the parameters related to the damping nonlinear term are unknown. This work is inspired by the approach firstly introduced for two-dimensional Navier-Stokes equations by Carlson, Hudson and Larios. We show estimates in L2 and H1 for large-time error between the true solution and the assimilated solution, which is constructed with the unknown damping parameters and observational measurements obtained continuously in time from a continuous data assimilation technique proposed by Azouani, Olson and Titi.

math.AP↗

arXiv2015

Existence and stability of global large strong solutions for the Hall-MHD system

We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global strong solutions is obtained with large velocities and small initial magnetic fields. Moreover, we prove the local-in-time well-posedness of $H^{2}$-strong solutions which improves previous regularity conditions on initial data.

math.AP↗