10 citations · 18 across the 6 of their papers we have counts for
6 papers
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 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…
Averaging of equations of viscoelasticity with singularly oscillating external forces
Vladimir V. Chepyzhov, Monica Conti, Vittorino Pata
Given , we consider for the nonautonomous viscoelastic equation with a singularly oscillating external force $$ \partial_{tt} u-κ(0)Δu - \int_0^\in…
Strong trajectory and global -attractors for the damped-driven Euler system in
V. V. Chepyzhov, A. A. Ilyin, S. V. Zelik
We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solu…
Infinite energy solutions for Dissipative Euler equations in R^2
Vladimir Chepyzhov, Sergey Zelik
We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this prob…
Totally dissipative dynamical processes and their uniform global attractors
Vladimir V. Chepyzhov, Monica Conti, Vittorino Pata
We discuss the existence of the global attractor for a family of processes acting on a metric space and depending on a symbol belonging to some other metric spac…