Davies, E. B. An indefinite convection-diffusion operator. (English) Zbl 1221.35260 LMS J. Comput. Math. 10, 288-306 (2007). Summary: We give a mathematically rigorous analysis which confirms the surprising results in a recent paper by E. S. Benilov, S. B. G. O’Brien and I. A. Sazonov [J. Fluid Mech. 497, 201–224 (2003; Zbl 1072.76027)] about the spectrum of a highly singular non-selfadjoint operator that arises in a problem in fluid mechanics. We also show that the set of eigenvectors does not form a basis for the operator. Cited in 8 Documents MSC: 35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 76A20 Thin fluid films 76U05 General theory of rotating fluids 76R05 Forced convection Citations:Zbl 1072.76027 PDFBibTeX XMLCite \textit{E. B. Davies}, LMS J. Comput. Math. 10, 288--306 (2007; Zbl 1221.35260) Full Text: DOI arXiv References: [1] DOI: 10.1017/S0022112003006633 · Zbl 1072.76027 [2] DOI: 10.1098/rspa.1999.0325 · Zbl 0931.70016 [3] DOI: 10.1103/PhysRevLett.89.270401 · Zbl 1267.81234 [4] DOI: 10.1103/PhysRevLett.80.5243 · Zbl 0947.81018 [5] Trefethen, Spectra and pseudospectra (2005) [6] DOI: 10.1002/cpa.20034 · Zbl 1055.15014 [7] Trefethen, Numerical analysis 1991 260 pp 234– (1992) [8] Shin, J. Phys 38 pp 6147– (2005) [9] DOI: 10.2307/2938670 · Zbl 0727.65072 [10] DOI: 10.1088/0305-4470/34/28/305 · Zbl 0982.81021 [11] DOI: 10.1112/S0024610704005381 · Zbl 1073.34093 [12] DOI: 10.1112/S0024609300007050 · Zbl 1043.47502 [13] DOI: 10.1007/s002200050521 · Zbl 0921.47060 [14] Davies, Linear operators and their spectra 106 (2007) [15] DOI: 10.1017/S0022112003007237 · Zbl 1134.76344 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.