38 citations · 182 across the 59 of their papers we have counts for
6 papers · 2 filters
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…
Preventing blow up by convective terms in dissipative PDEs
Bilgesu Bilgen, Varga Kalantarov, Sergey Zelik
We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type eq…
Upper bounds for the attractor dimension of damped Navier-Stokes equations in
Alexei Ilyin, Kavita Patni, Sergey Zelik
We consider finite energy solutions for the damped and driven two-dimensional Navier--Stokes equations in the plane and show that the corresponding dynamical system possesses a glo…
Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R^3
Anton Savostianov, Sergey Zelik
In this paper, we continue the study of the hyperbolic relaxation of the Cahn-Hilliard-Oono equation with the sub-quintic non-linearity in the whole space started in our pre…
One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrodinger operators
Alexei Ilyin, Ari Laptev, Michael Loss +1
In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson--Landau-type inequalities a…
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…