Layer potential methods for Vlasov-Poisson equation in parabolic Besov spaces

• Grant number: 10/12725-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2011
• End date: May 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Martins dos Santos
• Grantee: Jorge Luis Domínguez Rodríguez
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

We will investigate the existence and regularityof solutions for Vlasov-Poisson equation in parabolic Besov spaces, using the layer potential theory developed by R. Brown e Z. Shen (Rev. Mat. (1992); Ind. U. J. Math. (1995)) and the recent results by J. Rodriguez (doctoral thesis, UFRGS) and Tunde Jakap (v. T. Jakab e M. Mitrea, Math. Res. Lett. 13, 5 (2006)). We will need to define the layer potentials for Vlasov-Poisson equation and study the possible regularity yielded by them in parabolic Besov spaces. (AU)