Ilyin Aleksei Andreevich

Publications in Math-Net.Ru

1. Multi-vortices and lower bounds for the attractor dimension of 2D Navier–Stokes equations
   
   Dokl. RAN. Math. Inf. Proc. Upr., 516 (2024),  98–102
2. On a class of interpolation inequalities on the 2D sphere
   
   Mat. Sb., 214:3 (2023),  120–134
3. Estimates for the Dimension of Attractors of a Regularized Euler System with Dissipation on the Sphere
   
   Mat. Zametki, 111:1 (2022),  54–66
4. Sharp dimension estimates for the attractors of the regularized damped Euler system
   
   Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021),  13–16
5. Magnetic Lieb–Thirring inequality for periodic functions
   
   Uspekhi Mat. Nauk, 75:4(454) (2020),  207–208
6. Lieb-Thirring inequalities on the sphere
   
   Algebra i Analiz, 31:3 (2019),  116–135
7. On the Lieb–Thirring Constant on the Torus
   
   Mat. Zametki, 106:6 (2019),  946–950
8. On Strong Convergence of Attractors of Navier–Stokes Equations in the Limit of Vanishing Viscosity
   
   Mat. Zametki, 101:4 (2017),  635–639
9. On the closeness of trajectories for model quasi-gasdynamic equations. Linear case
   
   Keldysh Institute preprints, 2016, 090, 14 pp.
10. Lieb-Thirring inequalities on the torus
    
    Mat. Sb., 207:10 (2016),  56–79
11. Green's function asymptotics and sharp interpolation inequalities
    
    Uspekhi Mat. Nauk, 69:2(416) (2014),  23–76
12. A class of sharp inequalities for periodic functions. Addendum to the paper “Smooth solutions of the Navier-Stokes equations” by S. I. Pokhozhaev
    
    Mat. Sb., 205:2 (2014),  71–74
13. Lower bounds for sums of eigenvalues of elliptic operators and systems
    
    Mat. Sb., 204:4 (2013),  103–126
14. On a model system with a small parameter as a coefficient of the highest time derivative arising in the analysis of certain quasihydrodymamical systems
    
    Keldysh Institute preprints, 2012, 075, 9 pp.
15. On a model equation with small parameter as a coefficient of the second-order time derivative arising in the analysis of certain quasi-gasdynamics systems
    
    Keldysh Institute preprints, 2012, 012, 9 pp.
16. On the Spectrum of the Stokes Operator
    
    Funktsional. Anal. i Prilozhen., 43:4 (2009),  14–25
17. Attitude dynamics analysis of the first Russian nanosatellite TNS-0 using flight test results
    
    Keldysh Institute preprints, 2006, 018, 28 pp.
18. Lieb–Thirring Integral Inequalities and Sharp Bounds for the Dimension of the Attractor of the Navier–Stokes Equations with Friction
    
    Trudy Mat. Inst. Steklova, 255 (2006),  146–160
19. Algorithms of the magnetic attitude control system for the small spin-stabilized satellite
    
    Keldysh Institute preprints, 2005, 019, 32 pp.
20. Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations
    
    Mat. Sb., 196:1 (2005),  33–66
21. Orientation maintenance of a small spin-stabilized satellite
    
    Keldysh Institute preprints, 2004, 083, 26 pp.
22. Distributed on-board computer system prototype
    
    Keldysh Institute preprints, 2004, 025, 22 pp.
23. The software for the distributed on-board computer system prototype
    
    Keldysh Institute preprints, 2004, 014, 25 pp.
24. Principles of operation and design of the active-pixel sensors
    
    Keldysh Institute preprints, 2003, 085, 25 pp.
25. Image processing for the testbed vehicle navigation
    
    Keldysh Institute preprints, 2003, 073, 24 pp.
26. The russian small satellite for hyperspectral monitoring of gas pipelines
    
    Keldysh Institute preprints, 2003, 012, 14 pp.
27. Experience in the development, building and usage of a magnetic attitude control system for small satellites
    
    Keldysh Institute preprints, 2002, 053, 32 pp.
28. Analysis of the stationary viscous incompressible flow in a section of a pipe between two moving partitions
    
    Keldysh Institute preprints, 2001, 075
29. Recognition of the objects using data of Microrelief 3D-Detector (MDM-locator)
    
    Keldysh Institute preprints, 2001, 072
30. The mathematical processing methods of Microrelief 3D-Detector Data (MDM-locator)
    
    Keldysh Institute preprints, 2001, 071
31. Technical active 3D-vision system (MDM-locator)
    
    Keldysh Institute preprints, 2001, 062
32. Analysis of the two-dimensional stationary viscous incompressible flow in a rectangular domain with moving walls
    
    Keldysh Institute preprints, 2001, 033, 31 pp.
33. On the fractal dimension of invariant sets; applications to Navier-Stokes equations
    
    Keldysh Institute preprints, 2000, 022
34. Best constants in a class of polymultiplicative inequalities for derivatives
    
    Mat. Sb., 189:9 (1998),  61–84
35. Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides
    
    Mat. Sb., 187:5 (1996),  15–58
36. Partly dissipative semigroups generated by the Navier–Stokes system on two-dimensional manifolds, and their attractors
    
    Mat. Sb., 184:1 (1993),  55–88
37. The Euler equations with dissipation
    
    Mat. Sb., 182:12 (1991),  1729–1739
38. The Navier–Stokes and Euler equations on two-dimensional closed manifolds
    
    Mat. Sb., 181:4 (1990),  521–539
39. Stability of stationary solutions of equations of a barotropic atmosphere with respect to linear approximation
    
    Dokl. Akad. Nauk SSSR, 306:6 (1989),  1362–1365
40. Unique solvability of the Navier–Stokes equations on a two-dimensional sphere
    
    Dokl. Akad. Nauk SSSR, 301:1 (1988),  18–22