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On the global well-posedness of hydrodynamic models

Grant number: 18/22385-5
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2019
Effective date (End): February 28, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Anne Caroline Bronzi
Grantee:Ricardo Martins Mendes Guimarães
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

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)

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