A. Ilyin

发表

On the domain of analyticity and small scales for the solutions of the damped-driven 2d Navier–Stokes equations

E. Titi, A. Ilyin, 2007, math/0701530.

Sharp Estimates for the Number of Degrees of Freedom for the Damped-Driven 2-D Navier-Stokes Equations

E. Titi, A. Ilyin, 2005, J. Nonlinear Sci..

Stability and instability of generalized Kolmogorov flows on the two-dimensional sphere

A. Ilyin, 2004, Advances in Differential Equations.

STRONG TRAJECTORY AND GLOBAL W-ATTRACTORS FOR THE DAMPED-DRIVEN EULER SYSTEM IN R

V. Chepyzhov, S. Zelik, A. Ilyin, 2017 .

On strong convergence of attractors of Navier–Stokes equations in the limit of vanishing viscosity

V. Chepyzhov, A. Ilyin, 2017 .

On strong convergence of attractors of Navier–Stokes equations in the limit of vanishing viscosity

V. Chepyzhov, A. Ilyin, 2017, Mathematical Notes.

On the regularization mechanism for the periodic Korteweg–de Vries equation

E. Titi, A. Babin, A. Ilyin, 2009, 0910.1389.

Berezin–Li–Yau inequalities on domains on the sphere

A. Laptev, A. Ilyin, 2017, Journal of Mathematical Analysis and Applications.

On the fractal dimension of invariant sets; applications to Navier-Stokes equations.

V. Chepyzhov, A. Ilyin, 2003 .

Lower bounds for sums of eigenvalues of elliptic operators and systems

A. Ilyin, 2013 .

Lieb-Thirring Inequalities on the N-Sphere and in the Plane, and Some Applications

A. Ilyin, 1993 .

Lieb–Thirring inequalities on the sphere

A. Laptev, A. Ilyin, 2018, St. Petersburg Mathematical Journal.

On a class of interpolation inequalities on the 2D sphere

S. Zelik, A. Ilyin, 2022, 2204.12414.

Zero-mean interpolation inequality on the sphere

A. Ilyin, 2018 .

Lieb-Thirring inequalities on the torus

A. Laptev, A. Ilyin, 2015, 1512.01160.

Lieb-Thirring inequalities on some manifolds

A. Ilyin, 2011, 1104.2488.

Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier-Stokes equations

E. Titi, A. Miranville, A. Ilyin, 2004 .

Best Constants in Sobolev Inequalities on the Sphere and in Euclidean Space

A. Ilyin, 1999 .

ATTRACTORS FOR NAVIER-STOKES EQUATIONS IN DOMAINS WITH FINITE MEASURE

A. Ilyin, 1996 .

Navier-Stokes equations on the rotating sphere. A simple proof of the attractor dimension estimate

A. Ilyin, 1994 .

Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics

S. Zelik, A. Kostianko, A. Ilyin, 2022, 2202.01531.

Sharp upper and lower bounds of the attractor dimension for 3D damped Euler–Bardina equations

Alexei Ilyin, Sergey Zelik, Anna Kostianko, 2021, Physica D: Nonlinear Phenomena.

Dimension estimates for the attractor of the regularized damped Euler equations on the sphere

Alexei Ilyin, Sergey Zelik, Anna Kostianko, 2021, 2107.10779.

Sharp dimension estimates of the attractor of the damped 2D Euler–Bardina equations

S. Zelik, A. Ilyin, 2020, Partial Differential Equations, Spectral Theory, and Mathematical Physics.

Lieb–Thirring constant on the sphere and on the torus

A. Laptev, S. Zelik, A. Ilyin, 2020, Journal of Functional Analysis.

Green's function asymptotics and sharp interpolation inequalities

S. Zelik, A. Ilyin, 2014 .

On the Lieb-Thirring Constant on the Torus

A. Laptev, S. Zelik, A. Ilyin, 2019, Mathematical Notes.

A modified-Leray-α subgrid scale model of turbulence

Alexei Ilyin, Edriss S. Titi, Evelyn Lunasin, 2006 .

Attractors for the Two-Dimensional Navier–Stokes-α Model: An α-Dependence Study

Edriss S. Titi, E. Titi, A. A. Ilyin, 2003 .

On the dimension of attractors for Navier-Stokes equations on two-dimensional compact manifolds

A. Ilyin, 1993, Differential and Integral Equations.

Best constants in a class of polymultiplicative inequalities for derivatives

A. Ilyin, 1998 .

Lieb--Thirring inequalities on manifolds with constant negative curvature

A. Laptev, A. Ilyin, Timon Weinmann, 2023, 2305.10189.

Magnetic Lieb–Thirring inequality for periodic functions

A. Laptev, A. Ilyin, 2020, Russian Mathematical Surveys.

One-Dimensional Interpolation Inequalities, Carlson–Landau Inequalities, and Magnetic Schrödinger Operators

Alexei Ilyin, Ari Laptev, Sergey Zelik, 2015, 1502.01572.

Trajectory attractors for 3D damped Euler equations and their approximation

Alexei Ilyin, Sergey Zelik, Anna Kostianko, 2021, Discrete & Continuous Dynamical Systems - S.

A P ] 1 6 Ju n 20 21 SHARP UPPER AND LOWER BOUNDS OF THE ATTRACTOR DIMENSION FOR 3 D DAMPED EULER – BARDINA EQUATIONS

S. Zelik, A. Kostianko, A. Ilyin, 2021 .

Estimates for the Dimension of Attractors of a Regularized Euler System with Dissipation on the Sphere

S. Zelik, A. Ilyin, A. G. Kostyanko, 2022, Mathematical Notes.

Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

V. Chepyzhov, S. Zelik, A. Ilyin, 2015, 1511.03873.

On the spectrum of the stokes operator

A. Ilyin, 2008, 0802.4358.

Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$

S. Zelik, A. Ilyin, Kavita Patni, 2015, 1503.03415.

Vanishing viscosity limit for global attractors for the damped Navier–Stokes system with stress free boundary conditions

V. Chepyzhov, S. Zelik, A. Ilyin, 2017, Physica D: Nonlinear Phenomena.

Hyperbolic relaxation of the 2D Navier–Stokes equations in a bounded domain

Y. Rykov, S. Zelik, A. Ilyin, 2017, Physica D: Nonlinear Phenomena.

The Damped-Driven 2D Navier–Stokes System on Large Elongated Domains

E. Titi, A. Ilyin, 2008 .

A P / 07 01 53 0 v 1 1 9 Ja n 20 07 ON THE DOMAIN OF ANALYTICITY AND SMALL SCALES FOR THE SOLUTIONS OF THE DAMPED-DRIVEN 2 D NAVIER – STOKES EQUATIONS

E. Titi, A. Ilyin, 2007 .