On the global well-posedness of hydrodynamic models

• Grant number: 18/22385-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2019
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Anne Caroline Bronzi
• Grantee: Ricardo Martins Mendes Guimarães
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 22/00948-3 - On the self-similar blowup and existence of determining forms for fractionally dissipative fluids equations, BE.EP.DR

Abstract

In this research project we propose the study of the analytical properties of the solutions of equations arising from the incompressible fluid dynamics. Fundamental questions such as global existence and uniqueness of solution in some cases have not yet been answered and the purpose of this project is to advance on the understanding of such issues. We are interested in proving results of global existence of weak solutions, regularity and uniqueness of the solutions in Sobolev spaces, and also analyze possible scenarios of blow-up. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GUIMARÃES, Ricardo Martins Mendes. Estudo de soluções autossimilares da equação SQG generalizada. 2024. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.