Equations of micropolar viscoplastic fluids

• Grant number: 14/23780-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: April 14, 2015
• End date: July 13, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Martins dos Santos
• Grantee: Marcelo Martins dos Santos
• Visiting researcher: Vladimir Shelukhin
• Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

1 )Research: during the three months research stay at IMECC, Prof. Vladimir will work on research in order to develop a mathematical theory of micropolar viscoplastic fluids. It is a challenge to prove a global existence theorem. In contrast to Navier-Stokes equations, the constitutive laws are not regular. This is why a free boundary arises which divides a fluid and a rigid (plug) zones. One more difficulty is that one can not increase regularity of a solution highly due to irregularity of the stress-strain constitutive laws. First, we focus on weak solutions, which do not involve free boundaries. Our approach is different from that of Duvaut-Lions developed for the classical Bingham viscoplastic. We do not apply the variational inequality but make use an approximation of the generalized Bingham fluid by a Non-Newtonian fluid with a continuous constitutive law. 2) Prof. Vladimir will deliver a talk in our Differential Equations seminar during the first month of his visit and will interact with students, professors and visitors from IMECC, more particularly in the area of differential equations. 3) We plan that Prof. Vladimir will deliver talk in other institutes in Brazil, as IMPA, UFRJ and UFSCar, where we have contact with colleagues with common research interest. (AU)