Mapping Properties of Potential Operators Related to the 2D Compressible Stokes System in Weighted Sobolev Spaces

M. A. Dagnaw () and C. Fresneda-Portillo ()
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M. A. Dagnaw: Injibara University
C. Fresneda-Portillo: Universidad Loyola Andalucía

Chapter Chapter 5 in Integral Methods in Science and Engineering, 2022, pp 67-83 from Springer

Abstract: Abstract We derive a boundary-domain integral equation system equivalent to the Dirichlet boundary value problem for the stationary compressible Stokes equations with variable viscosity coefficient in an exterior 2D domain. To obtain the system of integral equations, we obtain integral representation of the solution using a parametrix. The solution is thus written in terms of domain and surface potential operators whose mapping properties are analysed in weighted Sobolev spaces. The main results relate to the equivalence between the integral equation system obtained and the original Stokes problem.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-07171-3_5

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DOI: 10.1007/978-3-031-07171-3_5

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