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.
[39]Dindo ˘s, M., and Mitrea, M.The stationary Navier-Stokes system in nonsmooth manifolds: The Poisson problem in Lipschitz andc 1 domains.Arch
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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.