38 citations · 182 across the 59 of their papers we have counts for
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Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain
Alexei Ilyin, Yuri Rykov, Sergey Zelik
A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possess…
Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions
Vladimir Chepyzhov, Alexei Ilyin, Sergey Zelik
We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain . We show that th…
Inertial manifolds for 1D reaction-diffusion-advection systems. Part II: periodic boundary conditions
Anna Kostianko, Sergey Zelik
This is the second part of our study of the Inertial Manifolds for 1D systems of reaction-diffusion-advection equations initiated in \cite{KZI} and it is devoted to the case of per…
Inertial Manifolds for the Hyperbolic Relaxation of Semilinear Parabolic Equations
V. Chepyzhov, A. Kostianko, S. Zelik
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing…