Establishes Fredholm and invertibility properties of the generalized Stokes operator Ξ and layer potentials S, ½+K on domains with cylindrical ends under positivity assumptions on V,V₀, yielding well-posedness for Dirichlet Stokes problems and small-data Navier-Stokes.
Homology of pseudodifferential operators I. Manifolds with boundary
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and evaluated in terms of extensions of the trace functionals on the two natural ideals, corresponding to the two filtrations by interior order and vanishing degree at the boundary, together with the exterior derivations of the algebra. This leads to an index formula which is a pseudodifferential extension of that of Atiyah, Patodi and Singer for Dirac operators; together with a symbolic term it involves the `eta' invariant on the suspended algebra over the boundary previously introduced by the first author.
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Well-posedness of a generalized Stokes operator on domains with cylindrical ends via layer-potentials
Establishes Fredholm and invertibility properties of the generalized Stokes operator Ξ and layer potentials S, ½+K on domains with cylindrical ends under positivity assumptions on V,V₀, yielding well-posedness for Dirichlet Stokes problems and small-data Navier-Stokes.
- Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis