Boundary-Domain Integral Equation Systems for Compressible Stokes Problems in 2D

A mathematical framework reduces Dirichlet and Neumann boundary value problems for compressible Stokes equations with variable viscosity to systems of boundary-domain integral equations. The paper by Mulugeta A. Dagnaw of Addis Ababa University demonstrates the equivalence and unique solvability of these systems in appropriate Sobolev spaces. The two-dimensional case presents special properties due to a logarithmic term in the parametrix, requiring specific conditions for invertibility.

Use Cases

• Developing numerical solvers based on the boundary-domain integral equation (BDIE) system described.
• Analyzing the properties of hydrodynamic single layer and hypersingular potentials for variable viscosity fluids.
• Studying the equivalence between BDIE systems and Dirichlet/Neumann boundary value problems in two-dimensional domains.
• Implementing computational methods for compressible Stokes equations using the parametrix-based approach outlined.

Strengths

• The paper provides a complete mathematical framework for converting compressible Stokes problems into integral equation systems.
• It specifically addresses the unique challenges of the two-dimensional case, including the logarithmic term in the parametrix.
• The work demonstrates the equivalence and invertibility of the proposed systems in Sobolev spaces.

Limitations

• Row count is unknown, which may limit suitability assessment for computational benchmarking.
• Column-level documentation is absent; field semantics must be inferred from the mathematical description.
• Last update date is unknown; freshness unverified.

Provenance

Source

Mulugeta A. Dagnaw, Addis Ababa University

Collection Method

Theoretical mathematical derivation and analysis.