×

An indefinite convection-diffusion operator. (English) Zbl 1221.35260

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.

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
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.