Existence and stability of large solutions for some fluid mechanics models

• Grant number: 13/21819-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): June 01, 2014
• Effective date (End): October 15, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lucas Catão de Freitas Ferreira
• Grantee: Maicon José Benvenutti
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we intend to study existence and stability of large solutions for some fluid mechanics models come from meteorology and geophysics, and associated to the large scale flows, such as Navier-Stokes Coriolis equations, Navier-Stokes-$\alpha$ Coriolis equations, and some quasi-geostrophic models.More specifically, we are interested in questions like: If a solution for one of these systems is global, then what happens with the solution for a perturbation of the corresponding initial data? Or for a perturbation of some parameter like the rotation speed or viscosity? Do we still have a global solution?Do we have some stability in such case? Answers to such questions will be sought via some known strategies for the classical Navier-Stokes equations combined with an analysis of dispersive effects due to rotation terms of the models. Other issues to be addressed in the project are related to the vanishing limit of some parameters and symmetries for such systems.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BENVENUTTI, MAICON J.; FERREIRA, LUCAS C. F.. Global stability of large solutions for the Navier-Stokes equations with Navier boundary conditions. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 43, p. 308-322, OCT 2018. (16/16104-8, 13/21819-8)