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The viscous vortex-wave system.

Grant number: 10/11176-4
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): November 01, 2010
Effective date (End): July 31, 2011
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Helena Judith Nussenzveig Lopes
Grantee:Eleonora Pinto de Moura
Home 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


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.

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