A generalized Stokes operator on cylindrical-end domains is Fredholm and invertible under positivity assumptions on V and V0 via layer potentials, yielding well-posedness for linear Stokes and small-data Navier-Stokes Dirichlet problems.
[42]Exner, P., Freitas, P., and Krej ˇciˇr´ık, D.A lower bound to the spectral threshold in curved tubes.Proc
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Well-posedness of a generalized Stokes operator on domains with cylindrical ends via layer-potentials
A generalized Stokes operator on cylindrical-end domains is Fredholm and invertible under positivity assumptions on V and V0 via layer potentials, yielding well-posedness for linear Stokes and small-data Navier-Stokes Dirichlet problems.