Well-posedness for Schrödinger-type dispersive equations

• Grant number: 24/19521-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2025
• End date: March 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Thais Ester Gonçalves
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project, we propose a study of some nonlinear systems and equations of Schrödinger type. We will analyze issues of local and global well-posedness and blow-up of the solutions. In the case of global solutions, we will also study their asymptotic behavior for large times. The ideas to be employed rely on recent techniques in the area of harmonic analysis and dispersive differential equations, including the concentration-compactness and rigidity methods. (AU)