The viscous vortex-wave system.

• Grant number: 10/11176-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2010
• End date: July 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Helena Judith Nussenzveig Lopes
• Grantee: Eleonora Pinto de Moura
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 07/51490-7 - Mathematical aspects of incompressible fluid dynamics, AP.TEM

Abstract

The vortex-wave system is a mathematical model for the behavior of 2D incompressible flows in which the vorticity has a continuouly distributed part who interacts with small regions of concentrated vorticity. This is a version of vortex dynamics for ideal fluids, introduced by C. Marchioro and M. Pulvirenti in \cite{Marchioro-Pulvirenti}. The main purpose of this post-doctoral project is to investigate the behavior of solutions of the viscous vortex-wave system when the viscosity is very small. We will also consider the related problems of approximating solutions of this system by desingularized vortex methods and by the averaged Lagrangian Euler equations. Our focus in this investigation is the critical regularity of the continuous part of vorticity which allows to pass to the limit in these different regularizations.