Free boundary 2D compressible Navier-Stokes equations

• Grant number: 08/08292-2
• Support Opportunities: Scholarships abroad - Research
• Start date: November 18, 2008
• End date: December 17, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Martins dos Santos
• Grantee: Marcelo Martins dos Santos
• Host Investigator: Zhouping Xin
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Chinese University of Hong Kong (CUHK), Hong Kong

Abstract

We consider the Navier-Stokes equations for compressible fluids with viscosity. Our goal is to show the existence of a solution in the presence of vacuum. We intend to solve the problem in dimension two. The three dimension case will be consider depending on the difficulty of the problem. We will assume that initially the vacuum is located outside the exterior of a bounded domain which boundary is a smooth curve on the plane. The evolution of this curve on time is one of the unknowns. Our idea to solve the problem is to use an iterative scheme that we designed joint with Zhouping Xin and Hailing Li last year (2007) during a visit we did to IMS-CUHK. (AU)