A. A. Ilyin, “On the Spectrum of the Stokes Operator”, Funktsional. Anal. i Prilozhen., 43:4 (2009), 14–25; Funct. Anal. Appl., 43:4 (2009), 254

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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 4, Pages 14–25
DOI: https://doi.org/10.4213/faa2962 (Mi faa2962)

This article is cited in 24 scientific papers (total in 24 papers)

On the Spectrum of the Stokes Operator

A. A. Ilyin

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Full-text PDF (210 kB) Citations (24)

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DOI: https://doi.org/10.4213/faa2962

Abstract: We prove Li–Yau type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier–Stokes equations.

Keywords: Stokes operator, Navier–Stokes equations, attractor dimension, Lieb–Thirring inequalities.

Received: 21.02.2008

English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 4, Pages 254–263
DOI: https://doi.org/10.1007/s10688-009-0034-x

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: A. A. Ilyin, “On the Spectrum of the Stokes Operator”, Funktsional. Anal. i Prilozhen., 43:4 (2009), 14–25; Funct. Anal. Appl., 43:4 (2009), 254–263

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Linking options:

https://www.mathnet.ru/eng/faa2962

https://doi.org/10.4213/faa2962

https://www.mathnet.ru/eng/faa/v43/i4/p14

This publication is cited in the following 24 articles:

Manil T. Mohan, K. Sakthivel, S. S. Sritharan, “Dynamic programming of the stochastic 2D-Navier-Stokes equations forced by Lévy noise”, MCRF, 2024
Federico Butori, Eliseo Luongo, “Large deviations principle for the inviscid limit of fluid dynamic systems in 2D bounded domains”, Electron. J. Probab., 29:none (2024)
A. A. Egorova, A. S. Shamaev, “Problem of the Distributed Control of the Emulsion Vibrations of Weakly Viscous Compressible Liquids”, J. Comput. Syst. Sci. Int., 63:6 (2024), 904
Alessio Falocchi, Filippo Gazzola, “The evolution Navier–Stokes equations in a cube under Navier boundary conditions: rarefaction and uniqueness of global solutions”, Calc. Var., 62:8 (2023)
Xueli SONG, Xi DENG, Baoming QIAO, “Dimension Estimate of the Global Attractor for a 3D Brinkman- Forchheimer Equation”, Wuhan Univ. J. Nat. Sci., 28:1 (2023), 1
Manil T. Mohan, “Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with “fading memory””, EECT, 11:1 (2022), 125
Baron A., “Determination of Hydraulic Resistance of Channels Using Spectral Geometry Methods”, Fluid Dyn. Res., 53:6 (2021), 065508
E. Ortega-Torres, M. Poblete-Cantellano, M. A. Rojas-Medar, “On the Convergence Rate of Spectral Approximations for the Equations of Nonhomogeneous Incompressible Fluids”, Numerical Functional Analysis and Optimization, 42:1 (2021), 91
Manil T. Mohan, “Wentzell–Freidlin Large Deviation Principle for Stochastic Convective Brinkman–Forchheimer Equations”, J. Math. Fluid Mech., 23:3 (2021)
Mohan M.T., “Global and Exponential Attractors For the 3D Kelvin-Voigt-Brinkman-Forchheimer Equations”, Discrete Contin. Dyn. Syst.-Ser. B, 25:9 (2020), 3393–3436
Storn J., “Computation of the Lbb Constant For the Stokes Equation With a Least-Squares Finite Element Method”, SIAM J. Numer. Anal., 58:1 (2020), 86–108
St. Petersburg Math. J., 31:3 (2020), 479–493
Alexei Ilyin, Ari Laptev, “Berezin–Li–Yau inequalities on domains on the sphere”, Journal of Mathematical Analysis and Applications, 473:2 (2019), 1253
Jin Ch., “Global Solvability and Boundedness to a Coupled Chemotaxis-Fluid Model With Arbitrary Porous Medium Diffusion”, J. Differ. Equ., 265:1 (2018), 332–353
Duy Phan, Rodrigues S.S., “Gevrey regularity for Navier–Stokes equations under Lions boundary conditions”, J. Funct. Anal., 272:7 (2017), 2865–2898
de Aguiar R., Climent-Ezquerra B., Rojas-Medar M.A., Rojas-Medar M.D., “On the Convergence of Galerkin Spectral Methods for a Bioconvective Flow”, J. Math. Fluid Mech., 19:1 (2017), 91–104
Jin Ch., “Large Time Periodic Solutions to Coupled Chemotaxis-Fluid Models”, Z. Angew. Math. Phys., 68:6 (2017), 137
Ilyin A., Patni K., Zelik S., “Upper Bounds For the Attractor Dimension of Damped Navier–Stokes Equations in R-2”, Discret. Contin. Dyn. Syst., 36:4 (2016), 2085–2102
B. Climent-Ezquerra, M. Poblete-Cantellano, M. A. Rojas-Medar, “On the convergence of spectral approximations for the heat convection equations”, Rev Mat Complut, 29:2 (2016), 405
Michele Coti Zelati, Ciprian G. Gal, “Singular Limits of Voigt Models in Fluid Dynamics”, J. Math. Fluid Mech., 17:2 (2015), 233

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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