Study of solutions to some nonlinear dispersive models

• Grant number: 24/10613-4
• Support Opportunities: Scholarships abroad - Research
• Start date: March 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Mahendra Prasad Panthee
• Grantee: Mahendra Prasad Panthee
• Host Investigator: Yuzhao Wang
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Birmingham, England

Abstract

This project describes the topics that we plan to undertake during the research visit to University of Birmingham, UK. The main interest is in considering the initial value problem (IVP) associated to some nonlinear dispersive equations. The first objective of this project is to study the well-posedness issues for given data in function spaces other than the classical $L^2$-based Sobolev spaces, the so called Fourier-Lebesgue spaces and modulation spaces. The next objective is to study the well-posedness issues for the IVP with given data in the Gevrey spaces that are analytic in a symmetric strip around the real axis of width $\sigma>0$ having holomorphic extension in the complex plane. In this context, we also plan to study the long time behaviour of the solution and the evolution of theradius of analyticity $\sigma(t)$ as time goes to infinity. Another objective is to study the behaviour of the solution to the dispersive equations from probabilistic point of view. Talking specifically, our interest is in considering the stochastic dispersive equations and analyse the behaviour of solutions. Also, we plan to participate in seminars and scientific meetings that may occur during the execution of the project to share the outcomes of the research undertaken.