Boundary Wave Propagator for Compressible Navier-Stokes Equations

We derive the boundary Dirichlet-Neumann maps for a model with linear compressible Navier-Stokes equations. Fourier and Laplace transforms are applied to derive the maps in the transformed space. A new classification of the roots of the characteristic polynomial in terms of their analytic properties is needed for the pointwise description of the inversion of the transforms using complex analytic methods. Algebraic manipulations reduce the transformed maps to a matrix of polynomials in characteristic roots over the ring spanned by rational functions in the transform variables and the global non-characteristic roots. This Normal-Tangential decomposition for the transformed Dirichlet-Neumann map gives rise to the new notion of a determinant for the intrinsic wave propagator along the boundary.