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Seminario: “Boundary-Domain Integral Equations for Stokes PDE System in $L_p$-based spaces for Variable-Viscosity Compressible Fluid on Lipschitz Domain”

Martedì 18 Settembre 2018, ore 12:30 - Aula 1BC50 - Sergei Mikhailov

ARGOMENTI: Seminars

Martedì 18 Settembre 2018 alle ore 12:30 in Aula 1BC50, Sergei Mikhailov (Brunel University London) terrà un seminario dal titolo “Boundary-Domain Integral Equations for Stokes PDE System in $L_p$-based spaces for Variable-Viscosity Compressible Fluid on Lipschitz Domain”.
Abstract
In this presentation we consider Boundary-Domain Integral Equations (BDIEs) associated with the Dirichlet boundary value problem for the stationary Stokes system in $L_p$-based Sobolev spaces in a bounded Lipschitz domain in ${\mathbb R}^3$ with the variable viscosity coefficient. First, we introduce a parametrix and construct the corresponding parametrix-based variable-coefficient Stokes Newtonian and layer integral potential operators with densities and the viscosity coefficient in $L_p$-based Sobolev or Besov spaces. Then we generalize various properties of these potentials, known for the Stokes system with constant coefficients, to the case of the Stokes system with variable coefficients. Next, we show that the Dirichlet boundary value problem for the Stokes system with variable coefficients is equivalent to a BDIE system.
Then we analyse the Fredholm properties of the BDIE systems in $L_p$-based Sobolev and Besov spaces and finally prove their invertibility in corresponding quotient spaces.