38 citations · 182 across the 59 of their papers we have counts for
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Recent progress in attractors for quintic wave equations
Anton Savostianov, Sergey Zelik
We report on new results concerning the global well-posedness, dissipativity and attractors of the damped quintic wave equations in bounded domains of R^3.
Infinite-energy solutions for the Navier-Stokes equations in a strip revisited
Peter Anthony, Sergey Zelik
The paper deals with the Navier-Stokes equations in a strip in the class of spatially non-decaing (infinite-energy) solutions belonging to the properly chosen uniformly local Sobol…
Attractors for damped quintic wave equations in bounded domains
Varga Kalantarov, Anton Savostianov, Sergey Zelik
The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimat…
Smooth attractors for the quintic wave equations with fractional damping
Anton Savostianov, Sergey Zelik
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is e…
Inertial manifolds and finite-dimensional reduction for dissipative PDEs
Sergey Zelik
These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as va…
Green's function asymptotics and sharp point-wise interpolation inequalities
Alexei A. Ilyin, Sergey V. Zelik
We propose a general method for finding sharp constants in the imbeddings of the Hilbert Sobolev spaces of order m defined on a n-dimensional Riemann manifold into the space of bou…